Ask Mr. Smarty Plants

Maybe, but Mr. Smarty Plants is wondering why you want to. Are you doing this to complement your greenhouse tomatoes?

For proper growth, plants need an energy source (light), a carbon source (carbon dioxide), mineral nutrients (usually from the soil), water, and an appropriate temperature. All of these conditions can be met in a green house. However, to sucessfully grow Zizania aquatica (Annual wildrice), you are going to need to approximate its natural growing conditions.

I have excerpted a portion of an article from the USDA concerning growing conditions. Click on the link to see the full article.

GROWING CONDITIONS
Physical and chemical conditions that appear best for the growth of wild rice in Michigan are:
1. Shallow clear water, 1 to 3 feet deep. 
2. Organic soil 6 inches or more in depth and preferably
with some calcareous material such as snail shells, etc.
3. A slight movement of water through the area during the
growing season. Best location is near the mouth of a
stream.
4. Fluctuations of water level less than 6 inches throughout
the growing season when the wild rice is in the floating-
leaf stage. 
5. An absence of carp Cyprinus carpio
6. Waters having a PH of 6.8 to 8.8; a sulfate ion
concentration of under 10 ppm and a total alkalinity of
40-200ppm.

I'm including several links with information about characteristics and growing of wild rice in the US, and its use in wetlands restoration.

University of Minnesota

Michigan Natural Features Inventory

Global Wetlands