Nope. Only magical diseases of significant power or insidiousness (like demonic plagues) should have any chance of that happening. Natural stuff will not.
And how would it evolve a resistance anyway if a Remove Disease spell wipes it out from a person's system? It's not like any of that stuff is going to survive the divine purging. Natural diseases only evolve resistances because they spend a while in the host's system before it uses antibodies or the like to fight off the disease. So it eventually adapts to the antibodies.
But magical disease-removal is rather more sudden and drastic; I'd only see a resistance build up, even in magical diseases, if the disease were magically engineered to do so (and engineered to be highly resistant in the first place, not to the point of actually having SR, but to the point of partially escaping a magical purge; some bits of the disease escaping when exposed to the magic, fleeing to another host body), or if the Remove Disease spell took something like a week to purge the disease (allowing some of it to escape as a result of simply having time enough to do so after exposure to some of the purging magic).