I don't know the answer to your question. But, if you are redoing the shower, I think rethinking the shape would be in order. I'd go at least a square space instead of the triangle shape you have now. Something like this...

Striking a Balance-Bathroom · More Info

It looks like manmade marble and no you can’t tile over it and when doing a bathroom reno it is best to take everything near where water down to the studs to make sure there is no mold and who wants an old grubby shower pan in a nice new bathroom

Have to ask if you are demoing room why would you want to keep pan? Not sure it would survive wall and floor demo anyway.

Just remove it if you are doing entire room.

I realize this is an old question but I am trying to do the exact same thing. Has anybody tiled over a shower base like this one successfully? Mine seems to be made out of concrete and in really good shape, but just 60's ugly. It would be much easier and faster to just tile over it. Thank you in advance.