I think the danger is that Hana would come to enjoy running the club. That's more than sufficient drama. Making her a house girl is merely an extremely unpleasant experience than can be endured and ended. Marring Hana's very soul is a lot more serious.
It's not impossible, but I think that would be a stretch. Hana is always going to oppose an external influence on her life, she's just ornery that way. But it's a very different thing to oppose internal influences. That's why Kathleen was so insistent on making this idea seem reasonable from Hana's point of view.
Hana only gets the shares if she takes an active role in running the club, and the club is inherently corrupting. If Hana has no stomach for it, she'll be forced to leave and thus be out of Kathleen's hair. But if she can stomach it, then it will be Hana who has to keep *herself* in line rather than Kat and Warren constantly riding herd on her. Either way, Kat wins.
Sure, if an opportunity comes up to get Hana involved in the exhibition I'm sure Kathleen will take it. But while I think that's Warren's big desire, Kathleen seems more interested in preventing Hana from doing something stupid while also giving herself a decent chance at gaining control of the club in the long term. Low risk, high reward.
Just because she's a twisted sadist doesn't mean Kathleen can't prioritize.
I see it similar. Hana "moonlighting" as a House girl to see if she likes it or not, is something she could endure or like or be indifferent to and can be ended as soon as she wants as she will be a part of the owners. Hana becoming corrupted/learning from Kath to enjoy running the club as it is CURRENTLY run, that would be the big danger for her.
As far as Hana's actions in Update 2, I think her grinding the MC is in keeping with their previous relationship: it only happens if the two are already intimate and spend another night together, so it doesn't need to lead to anything more. The issue is with the sudden jump to full-on sex the next morning. That's where I think the relationship advanced faster than it probably should have, possibly to set up the big cliffhanger. We'll know more when we see where the MC and Hana pick up the next time they meet, but my money is on Hana walking things back to a more ambiguous status.
I don´t think the jump to full-on sex/blueballing due to external situation is so sudden or too fast. To get to these events, you have to be rather committed to the Hana path. If the MC and Hana are just friends or a bit more, than you do not get these scenes, for instance Hana will shower and then come out fully clothed. Only if you are pursuing Hana, you´ll get the full event.
Therefor I see a return to ambigiousness only if Edwin and Hana are "just" friends.
I like the theory that there is an internal battle about the club ownership coming up in the future. Hana, MC and Jacob on one side, Kat, Killian and Warren on the opposition. August would probably go with his daughter but Chuck is a bit of a wildcard. He's nice to MC but some of the house girls are very afraid of him.
I too think that a battle for future "Headhoncho" in the club will be one big event on most, if not all playthrough variants. (Not all because if Edwin concentrates on just gaining one Carnation or getting money for his studies, Hana and Kath will be side theatre for this version of him)
But I would say that the two sides at the beginning are "just" Hana/Jacob on one and Kath/Warren on the other side. It will depend on how we play Edwin and the bromance with Ian, where these two will land. While the MC is trending towards Hana´s side in most scenarios and Ian towards Kath´s side, this is not set in stone. There is the potential to play the MC as a complete asshole, who would be quite at home on Kath´s side and I think a solid bromance with Killian would see him on the side Edwin takes. Which if we play the Hana path will be her side, even if Killian is not very fond of Hana.
August would side mostly with Hana, Chuck is far trickier to judge given what we know currently.