I think they definitely could.
Sancho might be able to tell that Sinclair has a thing for her, whether or not they got involved before while she lacked her most important memories. She might try to let things down more gently, if she thinks that it's not fair to him that he didn't really know who she was beforehand.
But whether they were involved before or after that was the case, I think she'd be amenable to possibly considering it now that she's awakened to her potential and wanting to do more for herself. And realizing that he'd be quite more serious regardless of what she actually is.