It may or may not work well, just depends on the throat length on the chamber. A short throated 6-284 will easily fit in a Rem 700 SA mag box with most bullets. Its tight with the tipped bullets or longer ogived match bullets but it CAN be made to work.
Alot has been said about seating the bullets deeper causing a dramatic drop in velocity performance. Will you loose some performance, yes, but it will not be dramatic if your using the mid weight bullets. With a heavy bullet or match bullet you have to seat the bullets much deeper then you would with the ones listed so it would not give up much velocity potential at all. A 6mm bullet in the 80 to 90 gr hunting bullet design does not displace ALOT of case capacity so you would likely do just fine as long as the throat is cut properly for that mag length.
personally, for the money, I would probably still have a wyatts 3.000" internal mag box installed just for added room and flexibility simply in which bullets you could use more then anything else.