No. For three reasons:
1. The professor in question is in the middle of an academic term and focusing on his/her classes, current students, research, publishing, conference work, department committee meetings, & etc. and your email at this point, having already applied, is just one more annoyance - no offense, but really, even if s/he is super excited about your application - you are not a current student, and s/he is trying to get through the first half of the term.
2. The professor in question may have absolutely no say as to whether or not you go to the admissions committee for review. S/he may or may not be on the admissions committee. The admissions committee will not see this email and therefore, refer back to #1.
3. You've already applied. Any further unsolicited communication now makes you look like a kiss-up, intentionally or not.
Just hang tight and trust the system. If your POI was interested in your work in October, s/he may have spoken with folks on the adcomm and asked them to keep an eye out for your application, dependent upon the size of the department. If you are a good fit, your application will be pulled for review. It's out of our hands now, and as much as that sucks, we have to accept it.
I will say, in the case of number, two, I know that from personal experience. I had been in contact with a very well-known (and very rare, Stateside) Celticist last year, and he was keen on having me as a student because of my interests in Old Irish, especially. After a flurry of emails it was determined that yes, he was taking on grad students and yes, I was the type of committed student he was most interested in having and no, my being an older student would not affect my application in detrimental fashion, in fact he preferred older students because they were usually doing it for a reason and therefore more committed than younger students who thought "Cool, I'll learn Old Irish" and didn't realize what that would entail. So I applied. After the admit season ended and I was rejected roundly from that program, I ran into him at a conference. He remembered my name and wondered why on earth I hadn't applied...I said I had, and had been rejected. It turns out the adcomm - which he was not on - had determined I didn't meet their GPA cutoffs in comparison to everyone else who applied. He never saw my application, and never had the chance to decide whether or not I was in. I can only imagine the consternation he might have felt if we had had further communication during the admissions season and this had been the case (and it would have been the case, it's a large department with limited funding, the adcomm makes the decisions). So...from personal experience, I say "nay" on communicating unsolicited at this point.