Yes but it gets even more convoluted than that. A bicycle brand doesn't even have to have won a World Championship to be adorned with the coveted rainbow stripes. It only has to be ridden in sanctioned competition by a reigning World Champion.

This loophole is made possible by the discrepancy between the World Championship year and the contract year. The World Championships traditionally take place during the last week of August or the first week of September. Consequently, a World Champion's one year reign typically spans two partial calendar years. However, rider contracts are typically calendar year based. After a rider has become World Champion it is quite common for them to switch teams to obtain a more lucrative salary for the upcoming season/calendar year. They take the rainbow jersey with them to the new team and if the bicycle sponsor has changed, that new bicycle brand gets to wear the rainbow stripes, even though it wasn't ridden to victory at the last World Championships.

Also, I don't how many of you have noticed this but even past World Champions get to wear the rainbow stripes in sanctioned races. It's not as prominent as the reigning World Champion, but in recognition of their past accomplishment, previous World Champions are permitted to display the rainbow stripes on the collar and/or cuffs of their team jerseys. Here's a photo of Hinault displaying the rainbow stripes of the cuffs of his jersey.