I don't think Spider-Man has to appear in an Avengers film but I do think his existence within the MCU needs to be established. The MCU feels really empty to me without Spidey being there. It would be like having a DC universe without a Batman or a Superman.
Spidey being in the MCU doesn't have to mean he will join the Avengers. He can still operate solo in the universe with only small cameos and easter eggs there to establish they're in the same universe (i.e. a Daily Bugle article on the table in an Avengers film). Even if he does appear in an Avengers film, it doesn't even mean he has to join the team. He could still have his solo films over at Sony where he is focused on his side of the Marvel universe but still help out the Avengers once in a while. Both Sony and Marvel would make a bit of extra cash from that.
If he will ever appear in a Marvel Studios film, my gut feeling is telling me it will be in Avengers 3. The reason I say that is because that's when Thanos will most likely be done. It took the entire Marvel universe to beat Thanos in the Infinity Gauntlet storyline. Assuming that Thanos will have the Infinity Gauntlet in Avengers 3, I can't picture just a couple of Avengers being able to beat him. I think the team will need all the help they can get. That's why I think Avengers 3 will be more of a Marvel Superheroes film than an Avengers film, and Marvel will probably try to get as many characters that they can get their hands on to battle Thanos. Assuming that Sony and Marvel still have the same good relationship they have now, I think that is when Spider-Man has the most chances of appearing in any MCU film.