There is a fair amount of traffic below RVSM on random routes, on the track routing, and on northern blue spruce routes.
The NAT tracks don't always start at the base of the RVSM airspace; published tracks frequently start at FL340, for example, and operation below that altitude without CPDLC can be done.
CPDLC connectivity issues aren't uncommon for Shanwick, and have been a problem intermittently for some time. If one is a CPDLC aircraft but has trouble logging on, one may or may not be asked to descend below the airspace; I've had both. Generally if one has CPDLC but has a problem logging on, it's simply voice reporting, per normal.
CPDLC definitely reduces workload over the traditional methods.