Spidey's not really a team guy, most of the time. The MCU shorthanded how long it actually took for him to be officially considered one of the Avengers, and that was only until well after he was an adult - the reason being that he's got enough problems juggling his personal life without trying to adhere to a group setting. 

That said, he'll absolutely team up with whatever team ends up forming if they need an extra hand. But he'll probably run off by the end of it, either because he's missed some personal commitment or because the police will chase him away because of some unsavory things that a certain newspaper publisher is about to get very spirited in claiming.

[i](Sorry that I haven't posted lately, been toying with how I want the next post to go. I know I'm missing the NYC event.)[/i]