Theory is one thing:
dust covers can contain/reflect internal microphonics back onto the lp surface, ’corrupting’ what the stylus receives/transmits.
play in up position? double check the deck remains level when the cover’s weight is all on the back when open. The cover can transmit airborne vibration via the hinges to the deck, could be worse. Can be less than ideal visually as well.
lift off? have a designated location, perhaps some felt buttons on contact edges, that’s my preference.
play closed? protects from airborne dust if a potential problem.
Reality is another. Can you hear any difference/detriment either way?
Do it blind first: turn your back, have someone else play it up, repeat the track closed, jump around a bit up/dn? After that do it yourself facing properly, your ’expectation bias’ will be reduced some at that point.