I think that a trans person could win, especially if his or her policies were more popular than those of the other candidates. The first barrier, though, would be becoming the candidate of one's party in the first place and that depends largely on whether the party leaders regard the would-be candidate as having electable personal qualities. That makes me ask the related question of whether a trans man would have an advantage over a trans woman.
In response to a question about who would win a particular election, someone, presumably in a bad mood, nastily replied
"People vote for the most macho candidate, even if it's a woman."
(It was me and I regret and apologise for saying it.) Nasty, snide, unfair and just plain false it may have been but I think that the electorate do tend to vote for someone perceived as strong willed and fiercely patriotic (occasionally with historically disastrous results).
Of course, womanly women can have those qualities, especially those who stand for office. However, do the electorate find those qualities more believable in men? If so, given that their policies were equally popular, would they be more likely to vote for a FTM trans candidate than a MTF one?
Come to that, would a trans man have an advantage over a cis woman?
