Companies were too small to have a band. Typically they may have one or two drummers and maybe a fifer. Could hardly qualify as a band. Prior to 1862 many regiments had bands, but most were abolished when the government ceased providing for them, putting the focus on fighting forces. Some did continue throughout the war. Some larger cities had bands with some military connections. For example, the Boston Brigade Band (their belts had the initials BBB) performed at many of the militia displays in pre-Civil War Boston. As for this piece in question, I feel there is really no way to prove it has actual military connection unless someone comes up with an identified hat or photo showing it. But if you like it as an old interesting piece worthy of further research and it is worth the purchase price to you, have at it. But just hoping it has a military, especially a Civil War connection, will not make it so.