Can theatrical experience replicate the experience of dreaming?

Yes, Breton thought theatrical experience could replicate the experience of dreaming.
Breton was a surrealist. Surrealism leaned heavily on the work of Freud, and especially his belief that dreams have meanings that reflect a structured and universal subconscious. In other words, though they seem random, dreams in fact use symbols and motifs that are common to everybody.
The surrealists, including Breton, wanted to capture the feeling and the symbolism of dreaming in the arts. They primarily focused on painting but also made forays into theater. Such theater replicated the dream state with vague settings, experimentation, characters acting in strange ways, the use of masks, and absurd plot developments. Everything in such a play is a little off-kilter, and illogical events occur, just as in a dream.
Breton liked the work of Guillaume Apollinaire, who wrote the dreamlike surrealist play The Breasts of Tiresias.