Asking potential advisor about their post-interview opinion on my profile for PhD application 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.
Typically application deadlines for fall admission are around December 1st; this timing gives the admissions committee time to review applications and have students interview at the university in Jan-Feb, with admission decisions coming in Mar-Apr.

I think the graduate coordinator saying spring admission is unusual might be a polite way of saying they don't really admit for spring; if you are applying to a program that is at all competitive, it isn't about not having red flags on your application, it's about being a stronger candidate than all but a handful of applicants.

If the professor you contacted isn't making a truly special effort to get you in for the spring, I don't think you should hold out hope for that. So far, everything you said - you had a nice interview, she contacted your references - sounds typical, not like she has taken an unusual interest in you that would allow you to bypass the typical admission procedures.

(note: you said you had your interview already; I'm assuming this was an informal interview with the professor you mentioned, and not an official interview conducted after you officially applied to the program)