This is a sort of random and quite specific question. I know that disease and Spanish rule decimated the populations of the Cuba, Hispaniola and the other Carribean islands that the Spanish settled very early in their New World adventures, to the point that pretty much all the native ethnicities of these islands are extinct, IIRC. What I'm interested in knowing is if these diseases had as large of a factor in the Spanish conquest as they did in Mexico and Peru.
Basically, did disease make the Spanish invasion easier, or was their conquest already pretty much a given by the time the diseases came into effect? Any answers would help me greatly with a TL I'm planning. Thanks.