In world 1-1, is it possible to reach the goal while you're in the background?
As you mentioned, the only white block in 1-1 is too far from the end of the level to get behind it with the crouching trick. The effect of going behind objects wears off by the time you can reach the goal. No guides or secret lists ever mention a magic whistle (or any other item) in 1-1 that can be obtained in such a way, even with glitches or hacks.
This link appears to show someone hacking the game to place a block near the end of 1-1 to find out if anything is hidden behind. I cannot guarantee this reflects an otherwise-unaltered game however.