Yeah, I feel like it would generally be an adorable couple teasing and play-fighting, buuuuuut the being made to stand outside the apartment topless holding chilled fruit in February for half an hour until she's seen by a couple of their friends and is literally in tears (on Valentine's day) was way too much, at least for the second strip. Not only is it too jarring and extreme to be effective slapstick, it's one of the first things we see of them, and sets a bad context for the more jokey stuff that comes after. Like, it hasn't even established itself as slapstick, by that point, and I think that's why a lot of the folks talking about unhealthy relationships saw it in that light; the tone of their relationship hasn't been established yet, the level of comedic exaggeration hasn't been established yet, the fact that it's supposed to be a comedy at all hasn't really been established yet, and then BAM, you get "you're such an embarrassment" in your face with no warning.
Really, even if it had already been set up like a Road Runner cartoon and the audience didn't have to make that jump on their own, I still feel like it fails as a visual gag. But at least it wouldn't give the rest of the story a bad aftertaste, if it just failed on its own.