I know they have already grown many different kinds of plants in space. The plants don't seem to care and will just head to the light. The plants them selfs seem to do just fine, how ever the roots can give them a problem.
http://science.nasa.gov/headlines/y2001/ast09apr_1.htm
"In an orbiting greenhouse, freely-falling plants don't feel the constant downward pull of gravity. As a result, water spreads out evenly in the soil-like material around their roots, which makes it harder for both air and water to reach the roots. Researchers had to choose the size of the granules in the "soil" very carefully. If the grains are too big, the roots won't get enough water; if they're too small, not enough air. "