An outlier should be Willie Currie, played for amateur Scotland, also played for Great Britain in the Olympics, the only Scot, some of this might have been while playing for Rovers.
Currie did get Scotland amateur caps whilst with Rovers and played once (I think) for the Great Britain Olympic team, but not actually in the Olympics. He played the first leg of an an Olympic Qualifier for GB at Wembley against Bulgaria in 1971, with the rest of the team coming entirely from non-league clubs in England. This was against a Bulgaria team which less than a year earlier had played at the Mexico World Cup (as Eastern European Communist countries claimed that all their players were amateurs). Amazingly, Currie helped the team keep a clean sheet and GB won 1-0.