Whether it becomes a staple franchise or not is tough to determine just yet. It certainly seems to have all the parts that one would need to see to suggest it's quite possible, yes.
But the problem with this is how you define a "staple" franchise. I can't even consider Splatoon a "staple" franchise yet, because a staple is predicated on a success with a sequel that isn't there yet. Is it super-likely to be one? Absolutely, at the very least in Japan. But it hasn't happened yet. When the eggs have all been hatched, we can count our chickens.
So how one defines a "staple" franchise is a debate that needs to happen first and foremost.
Do I think it will achieve Splatoon's level of sheer cultural cache in Japan? No, I don't. But I don't know if that's required, either. One can easily make a case that it isn't required. (see: Pikmin commercial theme song being inexplicably one of the most popular songs in Japan for a while)
Do I think it will obtain a large dedicated multiplayer fanbase for generations like Smash (and possibly Splatoon)? I honestly don't really know, because I haven't played it and can't because I don't own a Switch. But is that what defines a staple, where there are non-multiplayer games that also fit under that umbrella?
Do I think it will achieve the volume of sales or the attach rate that a game like Mario Kart can rake in? My gut says it won't, but my brain tells me that it's a pretty high bar and that ARMS may not have to aim that high to have that kind of staying power. There's a lot of Mario games that don't hit that threshold either, but Mario platformers are still considered a "staple" franchise. So does that mean it only has to achieve that distinction once to be considered a "staple"?
Until these things are defined, the conversation will revolve around differences in how people define what it takes to become one of those franchises, rather than the criteria itself and whether it can meet said criteria.