No problem at all
Yes, if you already have the wheel bearing and feel it's noisy, may as well put it in there. (when you jack up the rear driver's side and free=spin the wheel, hear anything? (though because one can only spin the wheel so-fast plus there's no weight on the hub/bearing, lack of noise doesn't necessarily mean the bearing is ok. If you've got it already, may as well replace it. And then the RDM filling you did is a must, it may have been dry and you caught it in time before serious damage set in.
After that, if you're still hear whirring but on the fence thinking of keeping it, I'd do one last thing and remove the propshaft (along with removing the fuses) and then test driving. The reason is those propshaft bearings fail on many Cherokees and when they do, they can sound like it's coming from anywhere (since they're bolted directly to the metal body). If you take the propshaft off and immediate the sound is gone, then you can either replace the propshaft (if you want to keep the Cherokee) or, by spraying enough brake cleaner into the bearing followed by spray multi purpose lubricant (e.g. PBblaster "blue" multi-purpose silicone), I've gotten the bearings to quiet down to where you could sell it/trade it.
ps: Sorry if this sounds convoluted! I just re-read what I wrote and it's probably not clear!!! LoL!