Yes and no, with blind guess your piston is usually made from composite aluminium, and a screwdriver is usually hardened steel. You can guess which one is harder.
If the piston just gets a small scratch then it is ok (usually), and most likely your spark plug hole will dented.
But the chipped part of the piston (if) could damage your engine further.
The cheapest way to get the chipped part or just to make sure it doesn't have any strange part on it:
- Open the spark plug, all of it.
- Remove the injector (nozzle) all of it.
- You can remove your exhaust (but it will make a mess)
Start the engine. The chipped or the trash should be out from the nozzle hole or exhaust.
If you are worried the chipped part is large and will damage your engine while starting it:
- blow with compressor, or
- remove the cylinder head (it's the only safe way to do it) and check it carefully.
If scratching the cylinder wall (piston cylinder / piston liner) the symptoms:
- A lot of smoke usually white (burning oil)
- Loss of compression (will make the loss of power and your fuel consumption increased)
- Loss of power
- Heat problem
- Loss of oil because the burning oil
But all of that could be none because the piston ring maybe still make it tight enough to close the scratch (still on tolerance).
To check if there is a loss of compression:
- Check your service manual or your car spec how much your engine compression (in bar or psi, not the compression ratio).
- Remove all spark plug.
- Install Cylinder Compression tester kit. Like this from AMAZON.
- Check the compression from the suspected cylinder. (crank the engine and see the max pressure)
- Compare with the other cylinder. Or compare with your specs.
So if your suspected cylinder has less pressure than the other, that likely needs service.