I've never owned a 340 (only 10/110s) but from the diagram the standard setup appears to freefloat the action, not the barrel (please correct me if I've mis-interpreted the diagram).
The 2 attachment point are rear at the recoil lug (at action-barrel interface) and from at the ring that you refer to.
If you want to aid accuracy I would first work on the stock so the wood, rear of the recoil lug does not contact any part of the action/trigger/mag assemblies;
So no, without modifying the action as above, you cant remove the barrel 'ring'.
Frankly, I dont thing its worth messing with it,other than my above suggestion, the idea of floating the action should theoretically aid accuracy, and 'bracing' the barrel doesnt necessarily detract from accuracy.... a free floating barrel will vibrate naturally while a fully restrained, say a sleeved barrel will not vibrate as it would be damped as such makes the shot more predictable....