You could find out.
(again, the cost of a replacement valve is not that high.)
best plan would be to replace the valve and see if it fixes the problem.
(assuming your issue is with the valve sticking)
but if you have your heart set on trying something new,
if you take the RCV out (after first recovering the R134a), and remove the center post, manage to re-install the valve properly, vacuum and refill the 134a, the system should operate at maximum displacement.
the car may be a bit harder to start.
this would likely cool the car, but only for a short while. before too long the evaporator will ice up, and no air will flow.
the system on these cars relies on control of the displacement to control pressures
sooner or later, the compressor will increase pressure in the system until something breaks, and then nothing will work at all.
exploding hoses are not funny.
other case is that the low pressure side flow is reduced to vacuum. this is bad because vacuum means no R134a coming in, and no oil coming with it. Lack of oil is not good. compressor can lock up.
The compressor design in these cars always has the shaft rotate.
unless the compressor locks up, then there is a mechanical disconnect (like a fuse) that is designed to break, allowing the pulley to continue to rotate so that the generator works, and the belt is not destroyed. (which could clog up the timing belt and kill your engine.)
how long it would take to break something will depend on how you drive. my guess is you would not get a week out of it.