That's like trying to propel your sailboat by holding up an electric fan.
To add just a tiny amount of nuance - sailing is redirecting airflow with a sail.
Surface and flow effects mean that very little air should be bouncing off the sail. If there is you probably have a lot of turbulence, and a 'bubble' will form around the sail around which most of the wind will simply divert, rather than redirect.
Or to put it another way, think of an entire parcel of air rebounding away from the sail, not individual air molecules.
Which, to bring it back to the origin of this thread of armchair physicists incorrecting each other, means that an LED mounted on a solar sail would not work, because the only force it imparts is collision. Which makes the sail analogy kind of a bad one for the use of solar pressure as a driving force.
Edit: Hmmm, but what if the surface material of the sail were phosphorescent and could gain energy state from the solar pressure, then kick it a photon when dropping energy state? And then what if there were a fly wheel (magnetic axel, in the vacuum of space, extremely low friction) that could act as the keel... Hmmmmmmm
Edit 2: I wonder if a lens that refracted light similarly to how air flows over an airfoil would create a "solar lift" effect? Unfortunately, lenses are heavy.
If it were possible to create a significant volume of thrust from photons emitted by LEDs, then you would be better off just pointing the LEDs away from where you wanted to go (like a rocket).