In a future setting like this, yes. The topic would need to be brought up for it to even be a character trait, and we're dealing with tech/bio advancements that'll makes such issues obsolete. The space within which a character would conform to contemporary perceptions of what defines a transgendered individual would be incredibly narrow.
I think you have a certain pre-conception of what a trans character would be and what their story arc and romance arc would be that's rather limited.
It is the future we're talking about. A future where, conceivably, medical science has advanced to the point where gender reasignment methods, either hormone based or surgical based, are quicker, easier, cheaper, more readily available, and have better results than the methods available today.
That is, of course, ignoring the fact that not all transgender individuals today go through such methods, and not all who do go "all the way" for complete reassignment surgery for various reasons. Sometimes out of fear of botched surgery and sometimes simply because they don't feel they need to. In the latter case, I don't see that stopping even with advances in medical technology. It's also assuming that the technology has advanced very far in these areas - medical technology in ME is better but it isn't perfect and hasn't overcome every hurtle, and it's established that there's also still social class separation in the future that might mean the technology isn't evenly available to everyone.
And of course there is the fact that we haven't at all explored what human society in Mass Effect thinks of trans individuals; one could take the general mum on the subject along with the acceptance of homosexual relations to say this is a nonissue, but some might argue that's something of a cop out answer.
At the very least, this idealized world where transitioning methods are easy and streamlined and society is perfectly accepting could be seen as an opportunity to cater to some wish-fulfillment for trans gamers, though conversations I've had with trans gamers in regards to fantasy settings tend not to like magical gender reassignment spells because they feel it minimizes or trivializes the reality of what they go through; same basic reasoning for why none of the super geniuses in Marvel or DC comics have come up with cures for cancer or AIDS; to avoid trivializing the suffering of real people.
I got to rambling a bit there, but the point is this; even if the methods are easier and society is more accepting, trans individuals are still going to exist. And given that Bioware hasn't laid down any lore on it, the assumption that it's gotten easier to the point of not being worth mentioning is just that; an assumption.