I’m not sure. In the case of “Dare to Be Stupid,” he apparently did play it for Devo’s founder, Mark Mothersbaugh, when it was completed, but before it was released.
The general sense I have is that he seeks to be respectful to other musicians, and doesn’t want to create hard feelings.
For the Doors parody (Craig’s List), Ray Manzarek played keys, so I assume he was OK with it.
I don’t know the general answer to your question.
Another style parody was Bob, a parody of Bob Dylan’s style, with the video a direct parody of Subterranean Homesick Blues.
To answer the OPs question, yes, obviously.
I think he’s a no-brainer, honestly, and arguably the worst snub in its history.
Their criteria isn‘t especially clear, but I’m not sure there’s many logical criteria you can build that he DOESN’T meet.
I think it’s fair to say their selection process is weird; they inducted the Sex Pistols, a short lived band unburdened by talent with limited commercial success and no influence you can’t also ascribe to a dozen other bands. But they had to be shamed into finally inducting Rush, and they still have not inducted Supertramp.
He absolutely belongs in the Hall of Fame. He elevated simple parody into a demonstration of true musicianship, and he’s been wildly successful at it for decades. To stay that culturally relevant for that long is a feat in and of itself.
He also gives a crazy good live show. One of the best concerts I’ve ever been to.
I don’t think that’s necessary. If it were the entire history of rock that is littered with songs that mimic more famous performers and want to ride on their coattails would have been eliminated.
I’m on the side of a broader RHoF. But I don’t think it matters in this case. The only reason that Weird Al wouldn’t qualify is that nobody truly imitates him: he’s a subgenre of one. There’s precedent for that even so.
With Dweezil Zappa on guitar.
I would say no, and I love Weird Al. It’s not enough to be clever or popular. Innovation, critical acclaim, influence are crucial.
FWIW, I’d exorcise probably half of the artists in the Hall—not because I don’t like ‘em necessarily, but because I just don’t think they matter enough.
Glad I could settle that 
…
Apparently, the guy who chooses doesn’t like Prog Rock, and Rush and Supertramp are at least prog rock adjacent.
Yup, and that’s been litigated here on the board a number of times.
Jann Wenner (founder of Rolling Stone and the R&RHoF) is apparently well-known for his dislike of progressive rock. It was generally believed (though without much, if any, empirical evidence) that this effectively blackballed a lot of prog and prog-adjacent groups from the Hall for many years. This changed at some point, maybe 15 years ago, and Rush, Yes, ELO, the Moody Blues, etc., are now in, but King Crimson, ELP, and Supertramp aren’t.
All that and more. Yeah Al needs to be there.
Hell, half the people in the Rock & Roll HoF don’t belong there. They are good musicians who have sold lots of records over many years but not exactly in R&R format.
That’s wild. I mean I can see how someone wouldn’t like prog rock, but how can anyone reasonably argue it’s not rock? And not influential?
I understand the votes aren’t there for Weird Al. It’s a shame because there are less deserving members who did have the votes.
I’d say that he has received quite a lot of critical acclaim, and is considered to be a strong influence in the industry, though in a unique way. YMMV.
As I think about it, I suspect that there are likely two main factors in why Weird Al has not ever even been on the ballot. Please note: I am not saying that these are good reasons:
Weird Al is a genius and should absolutely be in the HoF.
Agree. The only other person I can think of is Bob Rivers. He did some hilarious stuff, but he wasn’t in the same league as Al.
Agreed, I saw him on the current tour, and it was fantastic. It’s been so successful that he’s extended the tour. I strongly recommend going if a location and tickets are within your means.
To the topic of this thread, a very long time ago Al was interviewed, and answered something like he is more famous and has better staying power than most of the artists he parodies. If I’m remembering correctly, he was playing the character of Weird Al as being arrogant and superior. Even if the response was meant sarcastically, it was also 100% true.
Has that always been the case? It’s kinda hard to imagine a kid in architecture school calling up Freddy Mercury.
“Hello, Fred, I’m an accordion played and I was just wondering…”
I don’t know if Weird Al belongs in the Hall of Fame, but the induction concert would be epic.
Probably not when he was first starting out, true, for his early songs like “Another One Rides the Bus” and “My Bologna,” which got airplay on Dr. Demento before he had a record deal. But, once he started actually recording albums, it seems to have been the case.
Technically the Beatles aren’t rock and roll. I think we need to accept the museum and HOF is for the broad category of “modern Western popular music that isn’t country.”
“…except for Johnny Cash, Willie Nelson, and Dolly Parton.” 
No rational person would or could, but Wenner thinks Whitney Houston and Dolly Parton belong in the Hall, but ELP do not.