No, not safe at all. The longer you run the more chance you got of screwin somethin up. Your engine builds heat from not being able to get rid of the exhaust, so it starts building heat in an area that was never really meant to get That hot <that hot being a relative term with exhaust> It is fairly easy to check out, as 03Mopa said put your hand over tail pipe should be lots of pressure instantly if it dosent then chance are real good you got problems. If nothin else get a bit of straight pipe and pull the cat off replaceing it with staright pipe. Your truck will through engine codes but if it dont bog down then you found your problem, it it still bogs you can always put cat back on, eaiser if cat is slip jointed on and not welded.