I run off an SSD now days and noticed no time differences between computer builds. Combined with the fact that door skip has basically proven that the door loading animations are almost NOT required at all, I'm able to unscientifically, but confidentially say: No.

Especially if you're running vanilla, the animation is just there for cosmetic effect. It's not like the animation would speed up at all if you the game data were loading any faster. Hope that makes sense.

Door skip mod may be another story... but I don't think those categories will ever be SO optimized that it will matter, and as a result, we may never be able to break it down and tell. Unless someone is so inclined to TAS it up and do tests on both... But I would place my money on very negligible results.

I installed a decent SSHD in my PS4 a few months after I bought it. I compared one of my runs a long time ago to somebody else's run that has the original HDD. I didn't detect any different for the fade-in of room loading. I did detect a 1-2 frames difference for the fade-in of the menu however. Being very conservative, I calculated that it would only save at the most 7 seconds out of an entire run (for Jill any%), so it's not exactly some huge time save.

It's all explained in that boring thread:

http://www.speedrun.com/remaster/thread/cd7ag

No idea if that could lead to more time save on the PC version though.