Couple notes to share based on past experiences with this type of stuff....
CFL lights will work if you get enough of them and they are close enough to the plants. Light intensity decreases when the distance between the light and the plant increases. Since CFLs dont run hot, you can put em real close to the plants which helps.
Wrap the inside walls of the fridge with Mylar (mirror like reflective sheets) to help amplify the light the CFLs produce.
Get a fan. Plants grown with no breeze or wind can have very weak stems and tissues so try to "stress" the plants a bit to help toughen them up. Also helps with airflow and humidity issues.
Be ready for aphids to move in at some point. Have a plan of attack to manage them (like soap and water in a spray bottle).