It obviously depends on which screw it is, and the design of the board, but it's entirely possible. The case is used for what's called Chassis Ground, which is generally considered 'universal zero' as far as the circuit design is concerned. Since screws are typically used to connect the circuit ground to chassis ground, missing a screw where one is expected could cause a 'floating' ground (iow - not really ground).
Granted, most boards are designed with a ground plane, which would make a single screw unnecessary, but it's entirely possible that an on-board sound processor would be designed with a seperate ground plane. Using the main ground plane might introduce too much electrical noise for the sound processor to cope with, which could significantly reduce sound quality.
So yes, a single missing screw could very possibly mess up ground for your sound processor, and an imperfect ground means a very screwy system (pun intended).
BTW - If you were asking about Petej61's suggestion, I think he's referring to the possibility of a metal standoff on the case shorting out vias on the bottom of the board.