The first question to ask is, what kind of relationships can robots even have? How are they similar to humans, and how are they different?
Curly does care for the Mimigas, but was she programmed that way? A simple directive? Do they have a deep neural network? (Deep learning, seems similar to how people learn through trial and error, and build up experiences)
Or were they imprinted? Does it matter?
Well, I get the feeling with Curly's very direct, quick to trust and jump to the wrong conclusion personality; that she won't do anything beyond accidental innuendo.
She seems pretty innocent, so in her eyes, I'd say Quote is like an important comrade. She'll do anything to help him, just as she'll do anything to help the Mimigas.
Was her decision to give Quote the airtank a simple logic choice? She calculated you had better odds at making it out? Was there something else?
BLARGH. Well, in any case, she is either someone willing to go to extremes at the drop of a hat; programmed that way; or maybe she's just holding back something that isn't shown in the dialogue; but by actions like the iron bond, the air tank decision, trusting in Quote, supposedly knowing that he has amnesia. (He does still have amnesia even at the end, doesn't he? Cthulhu is the first one to bring it up I believe, and you don't even learn your name until using the Ma Pignon on Curly. You don't even contemplate about using it on yourself apparently. Though if the Jenka/Ballos dialogue is representative of returning memories, then maybe there's hope.)
Anyway, in all likelihood, the closest Quote and Curly will get in official Pixelverse is demonstrated in Wind Fortress:
That awkward moment when Curly is saved, and finds all around her bunches of naked Curly Clones.
"What happened here?? Was there a party!?"* ................ Yeah Curly... we had a ... blast.
*paraphrasing