I am not a biologist and do not know all the technicalities, but I agree in principle that DNA evidence could disprove common descent. This principle has been stated numerous time on these threads, always by evolutionists.
But there's a problem with the specific way you've stated your case. Darwin published 145 years ago, knew absolutely nothing about genetics -- a concept not yet invented, and classified descent by morphology. So the answer to your your question, in the exact words you have used, is no.
How does morphology explain fully functional genetic code skipping?