If you're talking about the Dawes Galaxy, I think it should be fine as long as the components are reliable enough and the frame is sound. Lots of randonneurs are happy to ride Rivendell lugged frames, and there is basically little difference between the materials used in those frames and the materials used in something like a Dawes Galaxy (Reynolds 531, if I recall). The Dawes' geometry should work nicely for randonneuring.

Right now, my primary brevet bike is an '84 Trek 610 (Reynolds 531CS) that is probably very similar to the Dawes--it has a mix of used and new components, all reliable. My "best" brevet bike is a Gunnar Sport, which differs primarily because it uses newer, higher-tech, thinner-walled, lighter steel tubing. The small weight savings is all but cancelled by the S&S Couplers, but I still like the way the Gunnar feels a little bit better, particularly for climbing. But for regular brevet use, I ride the Trek, because it's got all middle-quality components that cost less to replace when they wear out. The Trek feels very much like my Rivendell Rambouillet, which may go up for sale to help finance PBP if I can bear to part with it.