Probably, but that all depends on the thickness of the button. I would suggest sourcing a screw that takes in account the additional thickness of the strap button.
I'm not too keen on drilling it either, but I'm getting a little more than frustrated. I think I'll figure out another way to temporary fixing the strap (duct tape? some sort of suction cup?) to a position where I think i might want it and try it out first before I bust out my drill.
as for the the nose diving.... i have a strap that has non-slip backing, so nose diving or headstock diving isn't really going to be an issue.