I presume you mean a '30milliAmp Residual Current Device' or earth leakage circuit-breaker? These will be of little use, I think. Christmas Tree lights are usually without an earth connection and the insulating nature of the tree (and it would probably be standing in a plastic bucket on a wooden floor or on a carpet) means that it would be unlikely to pass sufficient current to trip an RCD.
The principle risks with lights on a Christmas tree are:
(a) bulb overheats because it is faulty or possibly because it is caught up in the foliage;
(b) bulb is broken and the naked filament is touching the foliage when the lights are turned on
(the filament will rapidly burn out in the open air once the lights are turned on);
(c) the cable covering is damaged allowing a short-circuit to take place within the set.
The best precautions are to see that:
1) the set is in good order before placing on the tree - all bulbs intact, no damage to the wires or bulb holders and a 3A fuse in the plug;
2) bulbs are clear of foliage as much as possible.
I would prefer to use lights supplied through a transformer, myself. This keeps the voltage low and isolated from the mains minimising the potential shock factor, and the transformer will limit the power that can be drawn, I hope, to rather less than that available from mains voltage through a 3A fuse.