yes 3126/c7 cat engines of the 2003 vintage do use a catalytic converter no they do not have EGR or selective catalyst reduction (SCR) or a diesel particulate filter (DPF)
If the tube between the air cleaner and engine is off and or melted it could be the source of the noise and needs to be repaired to keep dirt out of the engine but more important fix the the problem that caused the tube to melt, probably a leaking exhaust, also check the tubes and hoses between the turbo and the charge air cooler (CAC) and the CAC back to the engine, a small leak on these can make a lot of noise under a full load condition