I'm having a real hard time imagining that.
Dawn was created and programmed. So would Connor. Furthermore, he'd also have normal boy strength and fighting ability.
Though Connor, like Dawn, would have the ability to learn (ironically more so than some other characters) and apparently the monks couldn't program better self-preservation instincts into the human shape, he would not have been under the same brutal conditions and hateful indoctrination that he was in a Hell dimension with Holtz. So I'd see him as a bit more like Xander, though with "annoying little brother" emphasized.
I actually like this idea. Spike protects him as he goes to the Magic Box, acting like a scared boy trying to be brave when Glory has her (as opposed to putting up a fight with reckless insults as Spike would do) waiting for Buffy to save him, etc. I'm also curious if Buffy sacrificing herself for her little brother instead of sister would somehow be more controversial (to avoid derailing, I'll avoid the specific actual incidents that make me think this is a possibility).
Btw, I can't help but think of this scene...not a perfect match, but the demonic woman there speaking of "Oscar and Ozma" as Glory might "Dawn and the Key" (seeming more like a Hellgoddess to me) with the "Hound" replacing the magic snake (for the pedantic, the Hound that "follows up on the snake" if Connor was then hidden from her again as they ran, or after the snake failed as it did against Dawn)...I see Connor acting like that in this case, rather than how he'd act if he'd been raised (as a child of two vampires) by Holtz on a demon dimension:
Likewise, if Dawn was raised in that other dimension under Holtz then I'd see her as just as brutal in addition to having the fighting and physical capabilities as Connor (since she was born of the prophecy, and between vampires). I'd see her a lot like the Wishverse Buffy, at least when first stepping through onto Earth. I'm curious how the scene of Connor taking on that dealer and rescuing a girl that he was attracted to would play out as Dawn (it could still work, but it would likely have a very different tone and assumptions). I'm especially curious how Faith and Dawn would mix in this case.
I think in this case, if they're still going to use a mystical pregnancy, then Dawn would have to replace Cordelia in that regard (with more added in) which would almost certainly be even more controversial today than as it already stands (though then again, many who hate that story line think Cordelia and/or the actress deserved better, which would be different from someone just introduced, especially that irritating).
In short, as I try to imagine it, I see them as pretty much the same, just gender-flipped. It's the mystical pregnancy angle on Angel that would either be scrapped or drastically changed (because of what writers were willing and able to do with the material and keep it on the same station).