Yes, but it kinda seems like you would be able to see all of the photons "behind" you that will ever hit the event horizon after you've been there.

I.e. Immediately after crossing the event horizon, you'd be able to witness the end of the outside universe. However, the relationship between you and all of the rest of the stuff once it crosses the event horizon too, is what I'm finding tricky to define.

Thinking about it like this, it would seem that if you managed to cross the event horizon, from your perspective, everything else will now be inside the black hole with you, with only a difference in one-dimensional space quantifying your "times of entry."

The harder I think about it, the less clear the answer becomes.