... yeah major x to doubt. This goes beyond the confines of what this game is because its goal is to try to highlight aspects of the Pokémon games and while chasing a legend seems like a fitting idea since roaming legends are a thing... its clearly a big departure from anything in the games.
You have been producing some fun ideas but your hitting the point were your reaching for stars that aren't even there. In a respectful way I think you should turn it down a few notches and factor in how the game has operated so far into your brainstorming. Like a detail mentioned in the intro to the game is how the legends are isolated from other Pokémon, including each other in some instances. With that cavate it would be next to impossible for a legend to already know what your mission is. To not complete dismiss your idea this sounds like a potential thing for Arceus, but Arceus already seems to be complicated enough from what little details we know and also this scenario kind of throws the human pairing concept out the window which is important.
TL:DR probably a bit too ambitious of an idea here
Addendum: I'll actually be nicer here and mention a somewhat similar concept has already been mentioned by Chainsaw for tackling the Ultra Beast and Paradox Pokémon with them essentially serving as sub chapters after you return to the ship. No capturing these mons but it does have the MC go to the ship only to return to the region to chase down this other specific groups of Pokémon.