My father-in-law told me that his band director in high school put him on trombone for a year to help him play better on the trumpet. It sounds more to me like the director needed another trombone in the mix, but My father-in-law said it did help. Maybe it did, but maybe it was just another year behind a mouthpiece; I don't know. Anyway, later he was encouraged by friends to audition for Harry James, but he didn't follow through.
Personally, I notice neither benefit nor detriment to playing my horns. I just like being able to adjust to each of them, and I especially like hearing their different sounds.