I think that, in the last panel, Marten is well aware that Faye's issues go beyond getting blackout drunk, and is asking "she'll be OKAY, right?" because he wants the doctor to assure him that all those issues will be cleared up, not just her physical recovery from this incident. He knows that she can't actually give that assurance, but he's there on his own and worried out of his mind, and he doesn't have a friend there to give him a hug and reassure him that "it'll all be okay in the end" which is what friends generally say to each other in emergencies, even if there's no way of knowing it to be true. Unfortunately the doctor can't fulfill that role, but I think that's what he's asking for. I agree that Marten's natural tendencies would probably lead him to be an enabler, but there are several healthcare staff who will fill him in on why that's a bad idea, and once he knows what't best for Faye, I'm sure he'll do it.
I'm not convinced that going to NY would solve anything for Faye, even assuming that Angus would be interested in renewing their relationship. We already know that he had issues with her drinking when they were together, so this might have thrown any slim chance that they would get back together out of the window.
I would love to see Faye's mum show up soon, although I'm not sure that it's the type of hospital admission where phoning a parent would be the natural course of action--Marten may figure that Faye wouldn't want her mum to know that, you know, she got so drunk that she had to be admitted to hospital.