I have plenty recite poetry in their stream of consciousness, yet if I include a poem the character has written, I never put the whole thing in one burst, and always commentate on it.
In the post-modern movement, and now the post-post-modern movement, obscure mixes of style are common. Large parts of books like Pynchon's Gravity's Rainbow are written in verse.
A More interesting take on this is Nabokov's Pale Fire, which is written as a commentary on a 999 line poem, analyzing the poem compared to the life of the author, and the commentator.