Are we talking town celebrity fame, academic juggernaut fame, or Justin Beiber fame? We can tell you right now: No matter how good you are, you're not going to hit the level of Beiber fever. If you publish a book or two, you might certainly gain a level of fame as a published poet (which might even be harder to accomplish than becoming a major pop star), and there are those super poets like Mary Oliver and Nikki Giovanni that have millions of fans. However, it's more likely that the pinnacle of your success will be the solid respect and recognition of students and your academic peers in a university setting. Which is fine, though, right? We know you weren't thinking of getting into poetry for the money, so you probably didn't expect to become incredibly famous, either.
On the other hand, there are certainly famous people who write poetry, but that isn't exactly the same thing. Acting types like Suzanne Somers and Leonard Nimoy often assume—incorrectly—that being a celebrity means they're good at everything, including poetry. Illogical. Singer/songwriters and musicians usually have an easier go of it, but again, they're more famous for their sound, not their sonnets. Many people refer to lyricists like Bob Dylan and Bruce Springsteen and rappers like Kanye West and Mos Def as poets, and they're about as famous as it gets, but none of them became famous by writing poetry alone. It's quite possible that, without musical accompaniment, their words might never have reached the millions of people who have purchased their records. If they didn't write lyrics, Kanye West might have become a rap producer, and Bob Dylan and Mos Def might have become activists or politicians, so maybe they could have made it big regardless, but who knows. We have no clue what Bruce Springsteen would be doing right now if he weren't a rock star. Probably working a boardwalk game down at the Jersey shore.