If this was a TV show, she would undeniably be part of the main cast. But not only that. Since it's a dating sim/romance AVN, she has lot of romance time, sex scenes, and plot importance. I doubt that, if there wasn't the banner, Mr. DPC declaration about who the MGs are, and the report at the end of each chapter, one could tell she's not a main girl.
Yes, she'd be part of the main cast and here she is too, but she's a main cast member whose actions are, behind the scenes and under the surface, driving the story towards some very serious drama that will, eventually, impact and come into conflict with the MC, his way of life, and people close to him. You can somewhat romance her too, yes, but to me this is because it's an AVN. Plenty of games out there where you fuck and romance the "bad girls" because, at the end of the day, AVNs let you fuck anything that moves even if there's no ending with them. It's also probably part of a redemptive arc for her too later on.
Because Mr. DPC can define who are the main girls, but he can't define what an antagonist is, and Quinn didn't show traces of antagonism except in the first episode. An antagonist must be an obstacle in the protagonist's pursuit of his (or her, since, I'm talking in general terms and not only in BaDIK's case) goal or objective. Moreover, the antagonist, unless it's a beast or a force of nature, must be consciously and actively opposing the protagonist.
Antagonists don't always have to be in direct conflict against the protag and actively working against them in nefarious ways, they can simply be the character that creates the circumstances for conflict that will eventually ensare the protag because their bad actions bring this about such that the protag will have to face and deal with it. So in that regard, Quinn is very much a major driving force in bringing antagonistic situations into the MC's sphere that he will undoubtedly get roped into and have to deal with, even if he's not been involved with Quinn because these things will affect people close to him, and as an oftentimes selfless and driven MC when it comes to his friends, this will likely be his motivation to get involved.
No wonder we can barely detect what the main plot it (and, if there's one, we're still in the story introduction).
Overall I'd say the game is mostly a slice of life dating sim of sorts, but one that also has a lot teen dramedy to it as well. The main plot/drama in my mind is this slowly building danger where it comes to the schemes of Quinn causing problems and issues for those the MC is close to and the college at large. It's like a "hero's call to action" type deal where these dangers will need to be dealt with and ended before they ruin and cause more problems to the lives of others, and the MC along with other principle cast members will be the ones to do it. Much like TV shows that do the same thing, building up villainous threats in the background while most of the time, the main cast are unaware and unknowingly moving towards an inevitable conflct whilst also developing themselves and connections in ways that will be beneficial to that goal of putting these threats to an end.