Well, he needed the Beatles platform to launch his solo career- but his solo career is quite good.
I don't think he or John would have made it big without the other. George Martin said when he met them, they were not the greatest songwriters and he thought their material weak. Without the other, it doesn't seem like each would have progressed as far as they did. Paul at one point even considered dropping the Beatles and going into a "9 to 5" job, he probably would have and had a good career as a manager. God only knows what would have happened to John, but I'm sure Mimi would have set him on a path sooner or later, but it wouldn't be music- maybe the drawing career she already had set out for him.