Oddly enough, for nearly all existing video game characters, I really wouldn't enjoy it if they were gender-flipped; it would just change the character too much. But in the specific case of Link, he's always been strongly effeminate in his own way, as well as virtually asexual (and possibly actually asexual, but we really don't have enough data for that) and I think it actually wouldn't change his character *at all* to make him female.
I'm actually a bit astounded at how okay I would be with a female Link, because normally I consider gender to be an intrinsic part of a character, not just something you flip around to be PC or for laughs or anything like that. I think Link is an unusual, rare character in that my suspension of disbelief would barely blink at the idea of him being born a woman. Especially because, as MovieBob puts it, he's being reincarnated over the ages; it's not like you're having to rewrite his backstory, honestly.
Heck, now that I think on it, beyond Link being possibly asexual, it's entirely possibly Link actually *is* some form of genderqueer; we just wouldn't know about it. His sexuality and gender identity just never really come up in the games. (Though I haven't played Skyward Sword, so maybe it does in that one? I've vaguely heard it sort of might, though not very strongly, I think?)
You couldn't flip Zelda, though. She's a woman, through and through. Though I would LOVE to be able to play as her; no reason she can't kick some ass hand in hand with a player!