You can drive a 2005 Trailblazer 4.2L without the airbox cover, but you shouldn't do it for very long or very often. Driving without the airbox cover exposes the air filter to debris, dirt, and water, which can significantly damage the engine. This damage can lead to decreased performance, reduced fuel economy, and potentially costly repairs. The engine's mass airflow sensor (MAF) can also be affected, leading to inaccurate readings and potentially triggering a check engine light.
While it might seem like a minor inconvenience, it's best to replace the airbox cover as soon as possible to protect your engine's longevity and performance.