Is it allowed and/or safe to place objects on the dash in a PA28?
Next time you go flying just stick your hand up there and see if you can feel any suction at those holes when the engine is running. I doubt it. The holes in the coaming panel (the flat panel on top of the dash) near the base of the windshield are defroster outlets.

The vacuum pump on the engine accessory case sucks air through the air driven gyros on the instrument panel through rubber hoses interconnected to the vacuum instruments (on the Cherokee there is a regulating valve/manifold between the pump and the instruments).  On the upstream side of the instruments there is an intake hose with a cylindrical filter to filter the cabin air before the pump pulls it through the gyros.

The filter is mounted in the open below the instrument panel somewhere in the jungle of wires and tubes, on a bracket of some kind.  If you slide on your back and get your head under the panel, you should be able to spot a cylinder about the size of a small can of beans with a wire mesh around it and pleats like a car air filter.  That's the vacuum system filter. 

The main thing to be wary about when putting electronic devices on top the panel is they may or may not alter the wet compass when turned on.  Better to have an external antenna you can stick there and keep the GPS unit on a control wheel clip or something like that.