There are ways to do something like that, not exactly as you suggest, but close.
AFAIK, the VCAs only open when receiving signal from an EG.
The only other events that can trigger the EGs, other than a MIDI input (keyboard or other alternative controller), are Trig events from the internal sequencer.
There is a dedicated PLAY/STOP button for the internal sequencer, and there are "Sequence Auto-Start" and "Sequence Start Key" options in the System page that allow the sequencer to start without receiving a MIDI note (not described in the V1.0 manual as these options were added after the manual was written).
Therefore, this PLAY/STOP button can be used as a trigger.
- If you want repeated notes, you can let the sequencer run (similar to your idea of using the square wave of an LFO, except you have more control over sequencer events timing)
- If you just want to open the VCA, you can set an EG with Sustain and Release at the maximum and enable the HOLD key, so just starting/stopping the sequencer will trigger the EG that will stay "Open" until the HOLD button is disabled.
And yes, it is possible to assign the Joystick to pitch control and VGA gain control.
(you can assign the joystick axis to pretty much anything)