Will spilling a little liquid (beer, say) on untreated plywood for very little time damage or warp it?
Yes it can warp from liquid.  Will it in the case you mentioned - probably not.  Plywood will warp if you just let the board sit with moisture/humidity/gravity.  Until it is attached to something to give it shape (keep it straight) and it is coated, it will warp.  Get some bracing under your beer pong top to the plywood so it can't buckle, twist, or warp.