Star-occulting sensors

It was suggested recently that stealth in space might be countered by 
sensors that look for a stealthed vehicle randomly occulting a star, 
causing the star to wink out for a moment. This is an interesting 
concept, so I ran some very rough calculations to try and figure out if 
it makes sense. All figures order of magnitude only.

Assume the targets being looked for are 10 m.

Suppose diffraction limits the range to 1 million km.
Then the fraction of the sky occulted is (1e1 / 1e9)^2 = 1e-16.

Suppose there are 1 billion stars visible enough to be used for the 
purpose. (i.e. the target isn't careless or unlucky enough to wander in 
front of another galaxy, so we're using only the visible stars in our 
own galaxy.)
Then the probability of occultation is 1e-16 * 1e9 = 1e-7.

But the target is moving. So it has to travel 1e7 times its own length 
to have a reasonable chance of occultation.
1e7 * 10 m = 100,000 km, which is less than the originally assumed 
range, so the concept looks workable, unless I'm making a mistake
somewhere?

If the target is bigger, or you use shorter wavelength light (both of 
which seem plausible) then the range will be greater.