If you qualify for NEET then only you can sit in counseling. I am not sure if you will clear the qualifying cut off with 94. In case you clear you may sit in counseling but I wonder what the point to sit in counseling with just 94 marks.
Whereas participating in mop up round is concerned you can technically sit for that if you didn’t get any seat but definitely you need to attend first two counselings.
Hope this helps. All the best.