I have read that the chamber specs. of the 7mm Rolling Block are not entirely identical to the 7x57 Mauser as used in bolt action rifles. An excess headspace condition has been reported. This can be addressed by careful ammunition preparation.
The Colt/Browning M1895 machine gun was made in 6mm Lee Navy, I believe. Some were used at Peking, during the Boxer Rebellion, along with the rifles.
A consideration with RBs in the more modern smokeless calibres, particularly during that period, when ammuntion quality was not necessarily up to modern standards, is that a RB doesn't have the same sort of primary extraction that a bolt rifle has.