I mailed one professor inquiring about her research and possibilities of working with her if admitted through the graduate program (in US). We had a nice skype interview and she even obtained recommendations from my previous advisors. All of this happened before even applying for the PhD program.
I'm applying for spring and the graduate coordinator says that spring admission at their school is very unusual. So I'm kinda assuming that if the professor likes my profile, she might send out a word for me to the graduate committee. I'm confident I don't have any red flags on my profile, so if she roots for me then I should be able to get in. However, I haven't got any clear statement from her expressing that she will make a mention for me to the admission committee. Would it be a good idea to ask her about this? Because if she doesn't give me a mention, I really won't have any reason to apply to this school. But if she does root for me (and I do get in), then I'm definitely joining this school. And in that case I won't have to apply for fall admissions at other schools and I would save a lot of application money. Hence would it be a good idea to ask her about how she likes my profile and my chances of getting accepted, considering its an unusual time of the year for admissions? I kind of want to have an informal/indirect confirmation from her, without trying to come off as asking for too much.