Well of course, I should have known. Any machine with a logic board (like the CEI) will be looking at that switch through a timer window: if a "slow" coin holds the switch ON too long (in microseconds), it will trigger an error. So yes, you can use a pushbutton switch, BUT you need to poke that switch and release it very quickly. You might get the hand of it immediately, but it would be a problem for your guests.
Hmmmmm....; there's probably a simple way to insert a pulse-gate in line with the switch, such that no matter how long you hold the button down, it will only give a single instantaneous ON pulse.