No, on at least three counts. First and most importantly there's the relative angular size of the sun and the satellite as viewed. If you imagine looking at the satellite as it goes past the sun, it's much smaller, so it can't obscure enough of it to make a meaningful shadow. (By contrast, the moon is almost exactly the same angular size, so you can get a full eclipse.)
Then, even if the sun was a point source, you'd be close to or at being limited by diffraction. Just as the beam from a small hole in a screen blurs out into an "Airy disc", the shadow of a small object blurs out by the same amount for the same reason. If we guesstimate a largish 5 m diameter satellite at a close-ish 160 km with 500 nm light, you'd have about 16 mm (2/3") of blurring, but the shadow of a small satellite in a high orbit might wash out completely.
Finally you'd have turbulence in the air, which would mimic diffraction, but probably rather worse.
No man made satellite is big enough to cast a sun shadow on the earth. The best we can do is to see the outline of the satellite against the surface of the sun.