Yes, but would also be a terrible idea. One very quick and easy way to imagine is this way: The Sun shines on half the planet, with half the planet in sunlight, everything we know grows. Now imagine if the Sun shines on the entire planet, now the planet has roughly twice the sunlight. As well twice the light and heat energy, twice the UV radiation and possibly twice the solar flares.
The entire world would then quite easily turn into a water world, with the polar ice caps melting and the usual host of problems that brings about. On the other hand, this seems like a delightfully evil masterplan of some evil genius, disguised under the best intentions
EDIT: Changing questions, changing answers
As for the possibility of reflecting the light from the Sun with a single satellite, the physics checks out, you could assemble a gigantic, at least moon-sized space station, although it would need to be launched piece by piece and assembled in space. Performing the feat would be much much simpler, cheaper and easier with many small satellites instead.