The answer depends on how and what you qualify as a slow burn, but gut feeling, probably not.I was wondering are any of the LI in this slow burn out of curiosity. If not no biggie plan to try it anyways but just got curious.
Romance wise? Sure. The titular Carnations have hardly begun in that area.
Sex wise? As of Ch4Up2, the player hasn't gone all the way with one of the heroines yet, but he's also made her crawl around like a dog, potentially pissed on her face, and watched her drink a goblet of man batter. I suspect those might be qualify as above a simmer.
I do think there's a nice satisfying build up and pay off to Hana's relationship, but its built off an instant attraction and horniness. The thing that slows it down is circumstance, but I don't know if you'd call that slow.
In short, this isn't A Wife and Mother, you know?
Open the console and type hide screen qmenuDo you know if there is a way to get rid of the quick menu ?