I assume so.
An example of the trope I’m surprised not to see listed on the TV Tropes page is Designing Women, which had Jean Smart as the blonde, Annie Potts as the redhead, and Dixie Carter and Delta Burke as brunette sisters.
As for exceptions to the rule, Downton Abbey has a large cast that includes women with blonde, red, and brown hair, but I don’t believe there’s really a three-color trio. The three daughters of Lord Grantham are two brunettes and a redhead. If you take the three upstairs maids as a group there was often a blonde (Anna), a brunette (O’Brien), and one with reddish hair (Rose/Ethel), but O’Brien was both older and of higher status (lady’s maid instead of housemaid) than the others and didn’t work closely with them.
The three-color trio is perhaps the only cliche not used by Glee*, at least for most of the show’s run. For the first three seasons the glee club had six main female members, and they represented two cliques of three members each: the original performing arts geeks and the cheerleaders who joined later. Neither group consisted of a blonde, a brunette, and a redhead. The original choir members were all brunettes, although easily distinguishable because they were different races (white, black, Asian). For the cheerleaders, there were two blondes and a (Hispanic) brunette. But when three new girls joined at the beginning of the fourth season, one had blonde hair, one had reddish-brown hair, and one had black hair.
It’s hard to think of shows where three major male characters all have distinct hair colors. The guys of Friends all had dark brown hair. So did the guys of Seinfeld, and Elaine too for that matter. I guess there’s Modern Family, where of the four adult men there’s one with greying hair, one with dark brown hair, one with lighter brown hair, and one with red hair.
*I see that Glee is listed on the TV Tropes page, but whoever wrote the entry was really reaching. Of the three characters named, only the redheaded guidance counselor is in the main cast. The blonde and brunette were special guest stars. I don’t believe all three were ever even in the same episode.