I think my answer is definitely yes! Yeah, she has feelings for him o.O
The episode is complicated but that's what happened. When he saw the picture and she reacted that way It was a clear indication but the dialogue can make things clearer. She was angry because he considers his son is more important and because of his relationship with his wife
"If It were her you could stay" I would say It just a ridiculuos need for attention but why is she jealous of his WIFE? why did she change into her?
There is only one line makes It weird, when she said she "used to have somebody who passed time with her/" In this case It might seem she is angry because Rose is not around anymore. However there is not an explanation for her jealousy when he saw the picture and after in the end of the episode she gave him that picture and she was blushing when he thanked her.
Have you wondered why did she clear up the storage and at the same time she didn't throw away the content? He hadn't cleared that place up since Rose, this episode is about letting go the past, Amethyst and Greg were wathching that old show remembering old times. The storage is a metaphor for his heart/mind because the only thing left was the picture, a memory of Rose but now the storage is empty and he can get new stuff or he has "space" for the future/present.
I don't think Greg and Amethyst were in some strange physical relationship, watching TV seems be the favorite Sugar's activity to enjoy time together (Connie/Steven/Peridot and an interesting early comic by Rebecca about two brothers who watched the Simpsons their whole life) but I believe Amethyst has had feeling for Greg for a long time, Steven was 4 when they watched "lil butler" the first time, Amethyst always liked Greg since she took her hair style from his young version we don't know exactly when It happened but she has a kind of crush on him.