The plastic covering should not interfere with the mag stripe. In fact, cashiers have been known to use plastic (How Does a Plastic Bag Fix a Buggy Credit Card?) to fix finicky cards.
BUT, you technically cannot cover the signature. While it will still scan, if the cashier cannot see your signature and the CVV number on the back without obstruction, they may not be willing/able to take the card. Yes, it may still be readable, but if they refuse to take it you have no ground to stand on. (If you obscure the signature, at least make sure the CVV is readable or reprinted on top.)