I am applying for a consulting position and I emailed the recruiter prior to my application asking when was the deadline to apply. She responded to me giving me the information.
Now I submitted my application (with the cover letter addressing her), should I email her to tell her that I've submitted my application , to keep me in her loop when she views the applications for her region?
Assuming the recruiter is the same person that you submitted the application to then no you don't need to contact her to say you've applied. The fact that you've, well, applied will do that for you.
In your situation, I would not reach out to the recruiter again, since you've already reached out about the application deadline, it can be assumed that you will be applying before the deadline.
There are situations where a recruiter will specify "hey, let me know when you've submitted the application so I can forward it to the hiring manager" (or something like that), but you're not in that situation.
That's really up to you. There is no problem in doing so as it would be seen as a courtesy. (Often people turn off announcements from automated systems such as that application service as they are very good at filling one’s inbox.)
At the same time the HR person will most probably receive a notice and wouldn't take offence if you didn't directly respond either.
