The etymology of 'virgo' proposed by Ledo-Lemos, and rejected by Vaan (without further explanations), does not explain Lat. virgo as a compound from "*uiH-ro- (man) and *gʷén-eH₂- (woman)", but from *wir- 'young, youthful' (not 'man'!) and '*gʷén- 'woman'. According with this hypothesis, Lat. virgo originated as a compound whose original meaning was "young lady" (like German Jungfrau 'young lady > virgin').
Regarding the question asked here, the second segment of the word virgo is not the most important (i.e., if -go originate or not from I.E. *gwen- 'woman'). The pertinent to the subject at hand is if the first segment of virgo (uir-) was or not related with Lat. vir 'man'. If Ledo-Lemos hypothesis is truth, the response is: both words came from an I.E. root whose meaning was 'youthful, young'.
In a paper published in 2003, Birgitt Anette Olsen reached a very similar conclusion ["Fresh shoots from a vigorous steam: IE wih1ró-, Language in Time and Space: A Festschrift for Werner Winter on the Occasion of His 80th Birthday (Walter de Gruyter) pp. 313-330].
The following is the explanation as it appears in the article published by Ledo-Lemos in Indogermanische Forschungeng:
In Latin uir means “male”, and the same could be said of the vast majority of cognates that this word shows in other Indo-European languages (Old Irish fer, Gothic waír, etc.). However, there is a good reason to suppose that the original value of this element was “young”: in Tocharian A, the corresponding cognate (wir) precisely meant “young, juvenile” [cf. A.J. Van Windekens: 1976 1979, vol. I, pp. 574 575)].
It is fairly easy to understand that the adjective “young” would finally mean “male”. A parallel semantic evolution can be seen in the protoform that Pokorny [1959, p. 738] reflects as *merio (with the value of “young”, just as it still appears —among many other possible examples— in Greek μεῖραξ), but in Indo-Iranian it also acquired other values that closely remind us of the ones uir has in Latin: thus, in Sanskrit márya means “young, male, lover (masculine), free man” and the Sanskrit word maryaká and the Middle Persian mērak mean “male”.
The fact that the semantic value of the etymological group of the word uir would originally be “young” has interesting etymological consequences for other words, although studying them in depth would divert our immediate objectives and so we must limit ourselves to giving a brief outline. Since Schulze, it is generally admitted that there is some kind of relationship between the etymological group of the Latin form uir and the form uīs.
[NOTE: W. Schulze (1924), A. Ernout & A. Meillet (1959, words uir and uīs), A. Ernout (1954, p. 196). Also J. Pokorny (1959, pp. 1123-1124) seems to accept this relationship. However, this author also compiles a very unlikely etymology which connects uīs with uia.]
Of course, this approach still remains very likely but now we may be able to indicate that the etymological group of uīs would be better placed in the semantic field of “a vigour characteristic of youth” (by the way, this semantic value is still kept as such in the Sanskrit form váyas ).
Assuming this semantic value of “a vigour characteristic of youth” we can easily understand which is the origin of the Latin word uireō or the form uiridis for that matter.
[NOTE: G.R. Solta (1966, especially p. 47) has pointed out the morphological isolation of uiridis with regard to the rest of the Latin adjectives of colour: “Lat. viridis ist ein Außenseiter der Farbterminologie in formaler und semantischer Hinsicht, da es außer dem Farbinhalt auch andere Bedeutungskomponenten enthält”. Those “andere Bedeutungskomponenten” are of course, the meanings of “vigorous, young, healthy”. The subtle but important morphological differences between uiridis and the other colour adjectives can easily be explained, as is obvious, by accepting our hypothesis that the original semantic values had nothing to do with the colour. H.J. Vermeer (1963, especially p. 135), compiles many examples which prove to what extent uiridis and uireo were used in Latin even in contexts that explicitly prevented the meaning of “green”: “Andererseits kann das Farbverb seine Farbkomponente ganz und ganz verlieren, so vielfach in übertragener Bedeutung, wenn ‘virere’ nur so ‘jung, stark sein’ heißt usw.: inter niveos viridisque lapillos Hor S 1, 2, 80; virent metalla Mart 6, 42, 11 (…)”. This author explains such uses as a result of the loss of the meaning of colour, which he considers the original one. However, it is much easier to understand them as evidence that in classical Latin, the central meaning of uireō and uiridis was not in the semantic field of a particular colour but in “vigour, youth, strength”.]
It is also very easy to include the form uirga in the same etymological group: the original basis of its meaning (still clearly present in Latin) would have been “shoot, sprout” (a similar semantic evolution could explain the Sanskrit form vayāÏ “branch”).
[NOTE: Scholars have very often tried to establish a relationship between uirgō and uirga. It is a particularly old hypothesis, which already appears in G. Curtius (1879, p. 185); but Curtius himself refers to Corssen (1870, 2nd ed., Über Aussprache, Voca-lismus, Betonung der lateinischen Sprache vol. II, p. 521). It was quite successful during the last century (thus, for instance, among many other possible citations, K.F. Johansson: 1890, p. 438, note 2). This hypothesis is still compiled by J. Pokorny (1959, pp. 1133-1134) and it is taken into account by A. Walde & J.B. Hofmann (1965, word uirgō). A semantic evolution from “branch” to “young lady” is not impossible; but a priori, rather unlikely. Our hypothesis also establishes a certain etymological kinship which accounts for their formal resemblance, but in a different way: the original meaning of the element from which both finally derive was “youth”.]
In conclusion, we are bound to believe that the element *wir (o) originally meant “young” (as still happens in Tocharian); later it became “young male” (probably due to the semantic polarisation caused by the appearance of uirgō “young woman”), and it finally reached the simple meaning of “male”.
[NOTE: The word in Tocharian retains the adjectival value (it even has a feminine form with an a-stem), apart from retaining its original meaning. With regard to this, it may be relevant to remember the etymology compiled by Festus (W.M. Lindsay edition, 1913, p. 314, 15 16): femi¬nas antiqui (…) “viras” appellabant, unde adhuc permanent “virgines” et “viragines”. Despite the long-time belief, the form uira is not likely to be simply some grammarian's invention, because there is a Oscan collective noun form u(e)iro that means “persons, people”, which proves that the words in this family were not used exclusively in reference to men (cf. Eichner: 1985, p. 147). Thus uira could in fact be old and date back to the feminine form of the adjective originally stated as uir. In any case, the forms uirgō and uiragō cannot be put on the same level; uirgō was created in a very old age when uir still meant “young”, whereas uiragō has a more recent origin, it was derived from uir when this word already meant “male”, by means of a typical Latin suffix (with regard to this suffix, cf. A. Ernout, 1941).]