During the interview process, is it appropriate to reach out directly to people that work within the team I'm applying for?

I'm currently going through the interview process for a highly competitive position within my dream Fortune 500 company. I've been contact by a recruiter and had an introductory call with her to discuss the position/company and introduce myself. Pretty standard first round interview. During this call, she mentioned a couple times that the team was looking for some one that could join the company quickly (within the next month). I followed up with the recruiter later that afternoon thanking her for her time and she promptly replied letting me know that she would follow-up regarding the next steps at a later date once the team has reviewed all candidates. Fast forward a couple weeks... After not hearing anything, I reach out to the recruiter checking in on the application status. She informs me that the evaluation process is still on going and they've received hundreds of applications (!) and she does not know when she will have an answer for me.

So as I sit here waiting for an answer from the recruiter, my question is: is it appropriate for me to reach out directly to people that are working within the team I want to join? Or is this poor etiquette during the application process? I'm trying to find a way to differentiate from the hundreds of applicants but I also want to be mindful about coming off too strong. My plan was to reach out via LinkedIn or email.

Any feedback would help immensely!