I am not sure that you could cause autonomous mode to initiate through some signal to the competition port, but it would be possible to create an autonomous mode that ran off of the joystick. This is how i tested our autonomous.
I made my autonomous code simply a function. I called it once in the autonomous mode section, and once with an iff statement that ran only if p4_wheel was greater than a certain value. Here is an example.
Code:
if (p4_wheel > 200)
My_Autonomous();