Well, i can start with saying, I'm one of the few who actually liked Marc Webb's the Amazing Spider-Man. And really looking forward to the next!
Now, if they wanted to do a cameo (which that's mostly what fans want) it would work! I mean they are just doing a "Cameo" right? and not actually involving him in the same Universe (Did you loose me yet?)
Because realistically, Andrew Garfield's Spider-Man could never fit in the same world as the MCU Universe! OBVIOUSLY - They could make it work, i mean films can make anything work and have some sort of twist, even if that twist is awful, i mean think about it.
1. The events of TASM could be based before Iron Man 1.
2. The events of TASM could be during, or after the Phase 2?
Neither of those would work, Cause if it happened before, Tony Stark and Nick Fury would know who Spider-Man is because of everything that happened in New York with the Lizard, i mean.. something like that cant just happen and nobody hears about it.
Tony Stark - "Spider-Man? who's that"
Nick Fury - "That's classified for now.."
I'm not saying that's the way the scene would go, No matter which way, It wouldn't be able to be pulled off. I'm pretty sure after TASM. Everyone who watches the News, or has a TV would know who Spider-Man is.
There is no, NO, Way in hell that, that could be classified. haha
Why it couldn't work during / after, is because when they are in New York wheres the OSCORP? Haha, or where is Stark Tower?
Now i know I'm getting really into it, and maybe taking it too seriously, but I'm just saying.. It wouldn't work, Say so many years later and that's when TASM takes place, The world would still know about the Avengers.
It could have worked, but they would have to start planning from before Iron Man 1 even started, or after.. but it's far too late to involve Spider-Man (serious role wise) in the MCU.
LIKE I SAID BEFORE : They could always work around, Or do something, but i bet you money that it would be a super corny way of saying "Oh he was there the whole time, we just didn't know if we needed him" type of thing haha.