If this is regarding All India Counselling, no. You needn't necessarily have to participate in Round 2 of All India Counselling to be eligible for the Mop Up Round. Mop Up round is nothing but the round in which the vacant seats of Deemed Universities/Central Universities/ AIIMS/ JIPMER/ ESIC are filled up. The left over seats of Government Medical Colleges are transferred to the respective States and so no GMC participates in Mop Up Round. Eligible Candidates for Mop Up round:

1. Candidates who registered for Round 1 and opted for Free exit

2. Candidates who registered in Round 2 and exited with forfeiture of fees

3. Candidates who did not register for Round 1 or Round 2,

4. Candidates who registered either for Round 1 or Round 2 but did not get a seat

Candidates who have already joined in Round 2 of AIQ/Deemed/Central Universities/AIIMS/JIPMER are not eligible for Mop Up Round. https://mcc.nic.in/UGCounselling/Documents/UGSchemeFinal.pdf

But if this is regarding any State Counseling , please do help us with the State that you are enquiring about.