Would humans eventually evolve to fight off fatal diseases if we didn't treat/vaccinate for them?
Sure. 

When the Europeans settled the Americas, 90%+ of the native American inhabitants were wiped out due to diseases like smallpox that the Europeans clearly had developed resistance to. Clearly, the surviving native americans had resistance, and the Europeans had gone through some similar event previously in history.

The bubonic plague that was the cause behind the black death wiped out large percentages of populations, but selected for survivors with resistance:

Black Death Left a Mark on Human Genome

Caveats:


Often evolving to fight off disease involves mass death, like with >90% of the native american population dying.
There is always the chance that a future pandemic can come that human biology fails to simply evolve a resistance for and gets wiped out.
The Earth is changing rather quickly. The past is not a guarantee for the future.