most old turntables has a capacitor in parallel with the switch
They are called snubbers, and usually consist of a resistor and capacitor in series. Single package assemblies are available hence they may appear as single component only.
i think this is meant to suppress spark upon contact preventing deterioration of contact
On the contrary, they function during switching off and not during switching on.
however example if the switch is in the off position, isn't it that current will pass through the capacitor when charge is filled up leading to supply of current to the motor.
This will only happen if the snubber is defective.
then if the motor is not spinning, there will be a heat buildup in motor stator.
It depends on how defective the snubber is: the platter may spin as soon as you plug in the power chord even with the switch at off position; or after some playing time, the platter may continue spinning even if switched off; or after being left plugged for some time the platter may spin by itself (while switched off). Heat will build-up if the motor is mechanically prevented from spinning.
You can check for leaked voltage on the motor terminals. You can verify effectivity of the snubber by observing the switch contact for sparks while switching on/off in the dark.