Yes. As I said, I do that myself with a pfSense firewall/router into Unifi switches and APs with multiple VLANs and routing between them. I've also done it with an Edgerouter + Unifi switches and APs, and a Mikrotik router too. Of course the Unifi controller doesn't control a non-Unifi router, but you can set up whatever VLAN arrangement you want in the Unifi controller and then set up your router to match and do whatever inter-VLAN routing you want separately in its own interface.

It is not all nicely integrated together if you use a separate router (obviously), but it's not like it makes it impossible. It's not even difficult... at least not any more than it would be in any other setup.