Service tax- reverse charge

Hello fellas!!

I want to know if the liablity of service tax in reverse charge mechanism still remains if the service provider has not yet exhausted his basic exemption limit i.e Rs.10,00,000/- or hasn't been registered with Service Tax Department.

Example:- M/s A, a firm of advocates, has not got itself registered with STD, provides service to M/s B, who is liable to pay ST on Reverse Charge Mechanism. Whether M/s B would still be liable to pay ST as M/s A has not got itself registered?