If you're n Marching Band, absolutely. Requires alot of cardio work out, focus, and maintaining a healthy body as well as discipline. Check out some groups. Blue Devils, Phantom Regiment, Santa Clara Vanguard and many more. Its DCI (Drum Corps International).
I would consider it a sport because of the ability required for it. Along with competing. However, in school it counts as a PE credit because of amount of physical work it involves. Lots of running, and working out. Holding instruments, and playing while running and marching around the field for a 7-11 minute show.
Definition: 1.) Physical activity that is governed by a set of rules or customs and often engaged in competitively.
2.) An athletic activity requiring skill or physical prowess and often of a competitive nature
Marching Band definitely falls under that, so yes. It is a sport. However, just regular band, not so much.