Sorry if I wasn’t clear - you won’t be able to use the ADAT ports in that manner (the ADAT ports are for ‘digital’ connectivity, I’d forget about those for this discussion).
In answer to your question, yes, you can have multiple USB devices connected.
So, you’ll have one ‘audio interface’ (in this case your UR824) which you’ll set up in your Cubase device manager in the usual manner. That’s your sound card. You can also have another midi-to-usb interface - this will be a separate ‘device’ connecting e.g. the midi out on a keyboard (or whatever midi output you want to connect) to a different USB port on your computer. Once installed correctly, Cubase should be able to see this new device as incoming midi on a midi track (you may have to configure the device midi port setup). If you leave the midi track input as ‘all midi inputs’ you shouldn’t have too much trouble, unless you’re using multiple midi devices (in this case we’ve just got one - you could select the input for the midi track to be a specific midi device).
Hopefully a few people round these parts can give you a concrete example of what they’ve used and their exact configuration - it’s a very common setup!
I assume the reason midi connectivity wasn’t added to the UR824 is because a) it takes up more real estate and b) other standalone devices to do this are pretty chesp these days.
Does that make sense? If you’ve any more questions, fire away!