This answer is based on this question and answer concerning the classical names of the letters.
Given the pronunciation of a Latin word, there is typically a unique spelling (unlike in English!) so the exercise is pretty straightforward.
- ā: preposition
- dē: preposition
- ē: preposition
- ī: imperative of ire
- ō: interjection
- ĕs: form of esse
- tē: form of te
- ĕx or ĭx: preposition (ex)
No (with near hits):
- bē: noun bes, forms of beare
- cē: imperative cie
- ĕf: Perhaps one could argue that ex is pronounced as ef before a word starting with f, as in compounds we have efficere and others.
- gē: One might Latinize the name of the Greek goddess as Ge, but I have never encountered it or even Gaea. One would expect Terra or Tellus in this use.
- hā: If one argues that the initial h- is not pronounced, then this sounds like the preposition. But that would draw the very name of this letter into question. As cmw points out in a comment, this is used in Plautus for laughter, but it can also be seen as a part of a longer word hahae or similar, and the a is short.
- cā: —
- ĕl: —
- ĕm: This looks it could be an accusative for of is, but it is not.
- ĕn: interjection ēn
- pē: noun pes
- cū: pronoun cui
- ĕr: forms of esse, nouns era and erus
- ū: —
- y ([ī]) graeca: —
- zēta: —
There seem to be eight letters that are words.
As Draconis points out in a comment, some letters have alternate names (esse, elle, emme…).
These do not seem to bring any new letters to the list, but S gets a new word in esse.
This also produces the close hit ille ≈ elle.