Absolutely not.
I don't like this ship at all. And there's a reasonable explanation for that.
It was tossed in out of nowhere, with little evidence to back it up.
I mean, did these two even talk to each other or interacted in any way? As far as I could remember, Anemone hanged out with Ostrich the whole time. So, why didn't she fall for Ostrich? Sure, it would've been toxic as heck, since Anemone treats her like a servant, but it would at least make sense.
And, to further my point. If Anemone cared so much for Tamarin, why didn't we see a scene where she visited the RainWing after the explosion hurt her? She would've certainly have been worried if her crush was unconscious.
You see, we only know about Anemone's crush from Kinkajou, but we never get to see them together. There's an important thing called show, don't tell, or else it's harder to convince the readers to actually care about this relationship.
We are told that Anemone has a crush on Tamarin, but we never actually see it for ourselves, or hear her side of the story.
Which is why, I can't ship this at all.
Pros: I guess, if we get some screentime of them in the third arc, then maybe I'll change my mind. But for now, there isn't any pros.
Cons: Ship teasing: that's all it is.