No, it doesn't. The singularity inside a black hole is a future singularity, not a past singularity.

Just to clarify, you mean it's a future singularity in the entropy sense, or in some other sense?

Iff I understand correctly, what pdonis is saying is that it is in your future. It’s where (when?) you run out of future to go into, in a way which may or may not be analogous to the North Pole being the coordinate singularity where you run out of north to move in.

So it's the end of time in a sense?

That’s my understanding, but I’m just an enthusiastic amateur and that doesn’t take you very far with relativity.