No.....in the end you have to have that species to species leap for the evolutionary theory to be correct. The only means by which evolution can explain the variety of species is untold numbers of species to species leaps. We have no real evidence of that ever happening. In fact the evidence suggests otherwise.

A species can mutate till the cows come home but until the cows turn into something other than cows you still have nothing but inter-species mutation, which does not explain the variety of species and which is not evolution.