Yes!! The 4770 still has plenty of life left to live.
You could do w/ an upgrade to memory (not needed for Shadowlands but will make things feel a bit better when running multiple programs). I suggest 16GB as that’s kinda the gaming sweet spot and would only set ya back about $68 USD to upgrade, again this isn’t NEEDED but you will probably notice a difference when gaming and doing other things too.
That poor GTX 645 is extremely outdated and this is where your system fails requirements for SL. If I were a betting man I’d say this is the main reason why your system might feel underwhelming (while gaming at least, there is another reason I’ll list after this). Shop around and see what’s in your budget, a 1660 or better would make a world of difference.
It also appears you’re using a hard disk drive. Now is a great time to upgrade to an SSD (solid state drive) as they are fairly inexpensive. I would suggest a 500GB model, this will allow you to move your Windows install to it and a few games leaving your HDD for backup/steam library usage. If thats not’s in your budget then atleast a 250GB for Windows and WoW and if anything mentioned in this response will have the most notable impact of that system in general (in and out of games) it would be this.