Did you try? i did.
The controller UI shows you a hole in the left part of the diagram and explicitly tells you "no routing control without USG"
I have several Unifi switches and a controller (running on an rpi) on my network but I use my own router. I can setup VLAN access ports and trunks all day on the switches no problem, but I can't control the layer 3 routing between those VLANs with the controller, which is what you're talking about. By setting up a gateway/network on each VLAN from my router I can control routing. It's just not as slick as having a USG where it's all controlled via the controller UI.
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.