In the movie, "The Queen of the Damned", no, he doesn't, not really. The film's script tries to pair them but the chemistry and storyline is nowhere near realistic, so the ending scene suggests he did end up together with her but the storyline doesn't support it whatsoever. It depends on the viewer which part of the entire picture they see.
Even the producer of the film says it's "much less likely that Lestat would fall for Jesse than she with him." Which in this case is not that far from plain unlikely. As then he throws in "fate or circumstances" and "in a way he would never have predicted" - so admits there's no chemistry nor realistic storyline. Thus the film couldn't end like that in any emotional logic. The circumstances in question; it's Marius and Lestat they'd much more likely bring together (as father-son) and not Lestat & Jesse. And fate is always a card used when logic fails. They messed up but can't admit it. But at least they don't try to claim he'd actually love her.
And the source for that is on Warner Bros's Queen of the Damned website's F.A.Q.
However, in the books he had no love interest in her whatsoever.
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Yes, like his character in Modern Family, Ferguson is gay.
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