Well, yes. I've created in NWN some characters with whom I've had a lot of fun. Some because I got them out so nicely, other because she's so fun and I got so many laughs playing her.
Besides I have good luck to find portraits for those (not so much luck with portraits for male chars) and have good imagination to quickly translate from drawing/3d model to real girl who'd be represented.
Also because in playing I try to imagine the character and get inside her skin and at the same time it's not chars I play as being myself in any way so it's kind of another but I know her from inside and generally have something of the kind of girl I like.
So getting attached is kind of inevitable and necessary, if the char were one I couldn't get attached to and connect to it, I would not get to enjoy the game. In fact the reason every character I made failed because not having a good portrait caused me to not get the connection to get a feel of how they'd be and react and hence it would feel too much of a generic piece of imaginary pixels that I don't care and I don't know how would react.
Also those three chars I've got to like and feel attached to are also such that are aesthetically pleasing to me.
Of course that attachment doesn't mind any creepy thing like getting obsessed over them or develop feelings or whatever.
I would so like to cross them in the street, though, or knowing someone like them will or has existed. I cry in fetal position when I think they may not exist[/jest].
P.S. - Hazabaaza has felt attached, in my book. (man wouldn't have it been awesome without the comma?):
