Yes, all the pet names will become available. However, there is still this glitch (I think the warning message is still there), so there might be a chance that the account will clear a day early or late.

Also keep in mind the user could come back before it clears. I'd make a list of names so if you can't nab one you have others to consider
FINALLY GOT THE 15K WARDROBE DONE!!!!! Next up gutting and selling it.
Even if it clears, be aware that other people might also be after it, so you have to be quick on the draw. I lost a name by half a second because the site lagged as the name cleared.
I have a list a mile long, lmao.
I know. I'll probably be nowhere lucky enough to grab this name and I'm probably going to be totally adult about it and pout my ass off if I don't get it. The day it clears though (and the day before) I will be at work at the right time with a business T1 line under my control, so I should at least have that on my side. It's a name that's probably got a million and one people after it though, so I'm not really holding my breath. Still gonna pout though.