Bleh, knowing that WatXM is in the same continuity, I now believe Beast should be the only X-Man to ever appear in this show, ever. Maybe Nightcrawler. He was bearable in that show too.
I'd go for Colossus, who sat out most of that show. Hey, the Avengers could go fight a villain in Russia and he could randomly show up. It could happen.
And Vile is correct. Logan did technically appear in A:EMH, as James Howlett of the Howling Commandos during the micro's set in WWII.
Even the eyepatch is on the wrong eye for the Nick Fury of W&TXM. But, as said, it could have been an LMD. Lord knows I'd send one if I was trying to get the surly Wolverine to do anything (especially if I was tricking him).
On the plus side, it makes it easier to have Beast and/or Scarlet Witch appear.
Even if W&TXM is canon with A:EMH, we don't know at what point of W&TXM we are talking about. Does it connect to that show circa the end of Season 1? Or the start of Season 1? After all, in W&TXM, the X-Men were a pre-existing team who operated for years before "the explosion" split them up for a year, and then they all re-assembled bit by bit except for Colossus. Given Nick Fury's gray hair, that would imply that his meeting with Logan happened, at the very least, after the micro's ended (because he got the gray hair when Baron Strucker drained some of his life force with his Satan's Claw). But we have no idea, really. A newspaper claimed that the media was just catching wind of the existence of the X-Men's school, but the X-Men seemed to be fairly public knowledge by the start of W&TXM. One would imagine Steve Rogers would not be thrilled if he watched TV and saw giant robots and soldiers rounding up mutants for the crime of being different.
On the other hand, linking W&TXM and A:EMH opens up that story possibility, doesn't it? I never liked how in most of 616 Marvel comics, virtually no other superhero team gives a **** whether mutants are killed in the street or not. They never say one word about how wrong it is to be prejudiced against mutants or lift a finger to help them. That is somewhat appalling for the Fantastic Four, given that Reed and Sue's son is a mutant. The most the Avengers usually did was allowing 3 mutants to be long time members, but that's more or less the extent of it (and the way they treat Wanda these days, that's not saying much). Of course, there are franchise reasons for that. Marvel editorial liked to keep the X-Men books mostly apart from the rest of Marvel, and to a degree still do. If the popular heroes got the world to chill a bit on anti-mutie hysteria, the X-Men would lose a major source of story material. Still, it would open up an interesting episode where some of the Avengers face that sort of thing head on. It likely will come up whenever the show gets around to revealing that this is Ultimate Wasp, who is a mutant, but such a thing could include the X-Men as well. Like they could try to recruit Beast or Wanda and the public is aghast about it.