Would not having a air filter cause code p0410 in 2002 Buick redenzvous?

No, not having an air filter would not cause code P0410 in a 2002 Buick Rendezvous. Code P0410 is related to the secondary air injection system, which is a system that helps reduce emissions. The air filter is part of the engine air intake system, which is a separate system from the secondary air injection system.