Not really, climbing rope usually Dynamic rope is made to stretch and absorb shock. Sailing rope is meant to be very very stiff with little stretch. A Static rope used for rapelling may work but still likely has more stretch than you would ideally want for your boat.
Serious sailing and downwind racing I wouldn't. You would soon notice that the give in the line would slow you down. For casual fun sailing without concern for racing then use what you like. I don't recommend bungee
You must have discovered the awesome prices for sailing line.
As a sheet it might not be bad. I'm an avid climber and have tons of ropes lying around and have tried them out for sailing....when they get wet they stretch an annoying amount. Even static line (like a 6mm prussik line) stretches...i attempted to use it for my jib halyard on my first boat and as soon as water touched it....i just couldnt seem to get the jib tight enough. It'd work...just not be ideal. A 10mm rope as a sheet (specially if it's short) would be fine for casual sailing...just means you'd be sheeting in and out more. For all other purposes...stick with sailing ropes.