Answer:
Yes, sometimes. In most high school bands, there are clarinets and other woodwinds (flutes, piccolos, saxophones, etc.) It depends on the discretion of the band director. She or he may choose to only have certain woodwind instruments, like saxophones, because of their projection ability, and so on and so forth.
In some college bands, however, it's only brass and drums. There are independent pageantry organizations called drum corps that use entirely brass and percussion only.