That's not exactly right in terms of the description of a blackhole. A blackhole can have a singularity (there's formulations of blackholes without them), but i

That's not exactly right in terms of the description of a blackhole. A blackhole can have a singularity (there's formulations of blackholes without them), but it is not the singularity itself. As for the question of what it would with regard to the singularity inside a blackhole, my guess is nothing unless you make some fundamental assumptions that the geometry of space/time cannot collapse into an infinitely small and dense point. Because the notion of locality doesn't mean much to the idea of a gravitational singularity. They'll still exist just as happily in a non-local universe as they do in a local one if distances are arbitrary. Or rather I should say if geometry/shape is arbitrary for all objects. What makes them a royal pain in the butt is the fact the solutions meant to remove them often leave lots of other assumptions in the air that don't quite square with observations like loop quantum gravity (LIGO I believe knocked out one formulation of it recently). So, until we can find some observable phenomena beyond entanglement that makes it apparent locality and spacetime as we understand it doesn't exist we're going to have to trust the current models we do have.