While head gasket failures aren't *as* common in the 2004 Pontiac Grand Am GT 3.4L as in some earlier years of the 3.4L engine, they can still happen. The problem wasn't entirely eliminated across all model years. Several factors contribute to head gasket failure, including overheating, age, and general wear and tear.
So, the answer isn't a simple yes or no. It's less likely than in some earlier models, but it's not unheard of for a 2004 Grand Am GT with the 3.4L to experience a head gasket failure.