Comment by thusoy

Sadly, it doesn't. I was hoping for this as well, so I tested it, and it turns out that the user agent of the two browsers are identical.

  EME:      Mozilla/5.0 (Windows NT 6.1; WOW64; rv:38.0) Gecko/20100101 Firefox/38.0  
  EME-free: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:38.0) Gecko/20100101 Firefox/38.0