Chain transfer agents and rate of free radical polymerization
Not really.

As long as you are in solution (=unreacted monomer or solvent), it makes no difference if the reactive chain end is diffusing slow or fast. The monomer molecules come by at the same rate.

The mobile chain end would help against a local depletion of monomer, but once your mixture gets so viscous that this could happen, neither a long or a short active chain can still diffuse well (and neither can the transfer agent).

The only general difference you will see with transfer agent is that the Trommsdorff-Norish or gel effect sets in a bit later, because the overall viscosity of short chains is lower. In that sense, the transfer agent even slows down the reaction a bit. Which in that case is very welcome.

Of course the transfer agent radical can be either more reactive with the given monomer or less. (See "copolymerisation parameter".) So the chain restart can either be fast (in which case it makes practically no difference), or it can eventually be much slower. That depends on the specific transfer agent / monomer pair.