Depends on how bad things like texture pop are. Sure, it still runs, but it can get pretty bad. Especially if they have designed new maps around an SSD requirement, since open world games always seem to have those little "entryways" that just serve as visual roadblocks to buy time for assets to load in the background.
I'm sure people will moan about it, especially those who are still playing WoW on the toaster they bought in 2004 to play for release. But realistically, if you don't have an SSD by now, I think you've done something very wrong with your computer.