It's not possible that your 15th great grandfather is also your immediate grandfather (ie, your parent's father). But yes, of course it's possible to be descended from the same person/people on more than one branch. In fact, it's entirely expected - though not always recent enough that we can trace it but it's what's known as pedigree collapse:
https://en.wikipedia.org/wiki/Pedigree_collapseWithout pedigree collapse the population history of the world doesn't make sense.