Could a bad check valve cause crappy running?

Location
Las Vegas
I know having a check valve not let air in can implode the tank and starve the motor for fuel but will a valve that is broke completely (lets air in and out) not allowing the tank to pressurize also cause the motor to run bad? Or does it really not matter all THAT much that the tank is pressurized.
 

THRUST

ThrustInnovations.com
it usually have more of a hard starting problemn due to no fuel pressure . i have not noticed a bad running condition before . but replace it and test the part is so cheap .
 
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