Most certainly yes. There are many crazed and not so crazed approaches to this, and a wander round the forum will show all kinds of wird and wonderful constructions, mostly with encoders but some without, and I’ve run a zynth entirely in a field using batteries and a Hauwei tablet and a mouse ! Very interesting to compare mouse over to the tablet via VNC and the mouse connected directly to the GUI output 
Mounting a touchscreen in an environment seems to define the physical problems. I run a lot of 7" Standard’ Touch screens and thou I’d use them in a studio the methods of mounting them in a robust enough fashion for live work is more of issue but it sounds like you don’t see that as a problem so good luck and send us lots of pictures (and sound samples 
) of how it looks.
The control via external encoders is possible and indeed developing. We have keyboard bindings ( yes both types 
) for the GUI which do allow you to scroll in lists and such like, so you might well find that for remote running you need an enter and back key defined so perhaps they could map to specific keys ( or anything that makes MIDI) but if you end up choosing to provide switches for these function then you really might as well put on 4 encoders which take about as much install design as a couple of switches.
USB audio is not really a viable option but it’s a good way of testing a zynth…
Obviously if you are building a zynth into something else you will need to consider the mounting of the Pi and that needs to be in a corner of an enclosure to allow access to the sockets., and consider the audio connectors.
It’s surprising how quickly you end up as looking at the zynthian case as a pretty good answer. Subject of course to that long standing wyleu gripe, it’s not steel, so I can’t stick it to strong magnets and the annoying Pi people moving a couple of sockets on the board. It’s a good way of mounting a 3.5" screen with a set of encoders.
It also feeds Mofo