Nope I don't think so. If Edward had always been around she wouldn't have seen anything but him. But I actually like NM the way it is. Edward and Bella discover that they can't live without one another and it gives Bella a chance to experience a different kind of relationship but yet she still chooses Edward in the end. :)
THAT IS DOWNRIGHT RUDE! Jacob is not a stupid, obnoxious and disgusting mongrel. He is an amazing friend. Bella probably would have never fallen in pag-ibig with him if Edward hadn't left. But he did leave. Jacob didn't. He was always there for Bella when she needed him most. Edward wasn't. That's all I'm going to say.
First off, don't disrespect the character Jacob like that. If it wasn't for Jacob and his pack of "stupid, obnoxious and disgusting mongrels", Bella would have been killed multiple times while Edward was gone and Edward would have indefinitely killed himself. But no, she would not have fallen in pag-ibig with Jacob as long Edward never left. She was too in pag-ibig with Edward to pay attention to anyone else with him around. Jacob saved her from some of the pain Edward left, but if he'd never gone anywhere, that would have not have been necessary.