My first response would be "yes, the gender is the same as in Greek", but that rule definitely has exceptions. I wouldn't say that the general topic is very simple: I think that although there is a straightforward equivalence for many words, the words that show change or variation in gender are somewhat complicated to explain.
One exception that I know of is the neuter noun orichalcum which L&S says is from Greek ὀρείχαλκος. My understanding is that as a general rule, the names of metals were neuter in Latin (I first learned about this while researching an answer to an ELU question about element names ending in -um and -ium), so this may be the reason why the word was not borrowed as orichalcus.
The ending of orichalcum in Latin is also changed to -um match the neuter gender. Although you said that you're not interested in declension for its own sake, I'd say that declension patterns are relevant to your question, in that certain declension patterns in Latin are associated with certain genders. For example, the first declension is very strongly correlated with feminine gender, and even more strongly anticorrelated with the neuter gender. I know of only one neuter first-declension noun in Latin: Pascha, Paschae (from Greek πάσχα, which was used as an indeclinable neuter); it has both an alternative first-declension feminine set of forms (with accusative singular Pascham, nominative plural Paschae and accusative plural Paschas, etc.) and an alternative third-declension neuter set of forms (with genitive singular Paschatis, nominative/accusative plural Paschata, etc.).
So I would say that for a form like platysma, if it came to be used as a first-declension noun, it is very likely that it would also be used as a feminine rather than as a neuter or masculine noun.
And in contrast, I know of no non-neuter third declension noun with a nominative singular ending in -a, so I think it is very unlikely that someone would use platysma, platysmatis as anything but a neuter noun. (The category of neuter third declension nouns with a nominative singular ending in -a is as far as I know exclusively used for Greek loans, but there are a fair number of these words in Latin, almost all from Greek nouns with the suffix -μα.)
Aside from orichalcum, the book Dynamics of Morphological Productivity: The Evolution of Noun Classes from Latin to Italian, by Francesco Gardani, mentions Latin cerasus f. from Greek κερασός m. and bracchium n. from Greek βρᾰχῑ́ων m. Gardani says that for nouns that have multiple forms and genders in Latin, "The coexistence of two gender values proves, on the one hand, the normative tendency to follow Greek use in literature and among bilinguals, but on the other hand, a tension towards normalization and morphological integration" (p. 358).
