Historical precedents have been mixed. Games consoles have been allowed to retain exclusivity for software but not hardware (controllers, etc.). Printers haven't been allowed to reject third party refills.
The only way for there to be a clear judgement would be a trial.
I'm sure I can find the cases if there were some, so please don't search for them if you don't know them off hand.
Thanks again Dan
SEGA only wanted licensed developers to develop for the Mega Drive, so they required a piece of code in order for a game to boot. This piece of code included the SEGA trademark. The thought was that if any unlicensed games appeared, SEGA could sue for trademark violation. SEGA sued when Accolade started producing unlicensed carts for the Mega Drive. The courts ruled against SEGA saying that since the code was functional, not expressive, there was no trademark violation.