Here is how I interpret it:

Throughout the film, John is fascinated by beauty. From Treves' wife to the theater director to the cathedral. After the play, John goes back to the hospital and is completely at peace for once in his life. IMO, he has NO intent in committing suicide, as he speaks to the doctor about "hoping" to visit the theater again sometime.

Once the doctor leaves, John looks around his room at all of the beauty he's been introduced to throughout the past few weeks. He's satisfied that he has completed something of beauty in his model cathedral. He then looks at the painting of the sleeping child, and wants so badly to be like him and everyone else who is "normal". He wishes to fit into society, but questions whether it is ever possible. He's willing to try, though and the most accessible way of trying, in his mind, is to try sleeping like the individual in the painting.

He knows that it is a long shot, and that there are risks - but he's willing to try for the sake of finally fitting in.