you need some venting from somewhere, either a vent line or the filler cap.

as gas comes out and is used by the engine, air has to get in somewhere, or you get negative pressure/vacuum inside the tank, eventually this will suck back harder than the pump can pull forward, and the fuel flow to your engine stops until the pressure is equalized.

so yes, if your tank truely is not venting, it can cause problems with your engine.