This should be clarified in local procedures - not good if individual controllers use different techniques and procedures on the same sector.
One problem with it - most crews may still assume they are under radar control, even though you haven't stated it - because they normally are in this sector. Also, if someone calls for wx diversion or anything similar, it might be easier doing it, having him under radar control.
I'm not sure if doing part of the sector procedurally really helps to relieve workload, but I'm not an area guy.