Was the trip necessary?

I think so. Father and son really needed it.
If Max came clean about his date with Roxanne at the first minute or if Principal Mazur never called Goofy, thing could have been worse. The trip at the Possum Park, for all its awkward humiliations, did prove how big the rift Max had with his dad. Goofy had no idea how to relate with his son, and Max didn't want anything to do with Goofy. The trip allowed them to bond and learn about each other.
It definitely helped Max. The character at the beginning would have NEVER considered introducing Roxanne to his father or, once winning her forgiveness for lying, would NOT delay his big date over some prior engagement with Goofy. The kid needed to get his ego crushed a little. Think of the alternative: Without the trip, Max would never have resolved his issues with dad. Heck, the popularity-rise he got from his Powerline performance could have increased his arrogance. Reaching his way up in becoming part of the IN crowd, Max might be pressured to sacrifice anyone that might endanger it: and I'm not talking about just his father. I would bet Max would have dumped PJ as his friend and practically ignore the guy unless it was for some sheepish ridicule to gain his new IN friends favor (PJ would be doomed without Max). And since Roxanne actually liked the old Max, she probably would have dumped the new prick.
So even if it was a cure worse than the disease, Max needed the trip.