Hii

No you can not directly apply to the second round and mop up round of counselling of NEET. 
It is a step wise and organised process. You have to first participate in 1st round of councelling and incase you do not get a seat or you opt out of a seat by informing the authorities in time, then you can proceed for 2nd round and accordinly in the mop up round as the case would be.
There is no option of going directly to the 2nd round.

Hope this helps
Thanks!