I'd be skeptical of it. It can be done sure, but it may take alot of light and an elaborate set up. I've seen people box in tomatoes and have lights above and on each side of them.

You can grow tomato seedlings to about 6" tall (4-6 weeks old) under fluorescents. It's a good way to start them in spring for planting after the soil warms up.

You could maybe grow them to maturity with a fluorescent "light cube" as mkiker describes, but you'd be burning as much electricity as an HID light.

Yup, you can grow them to maturity under fluorescents. Just don't expect them to produce as much as if grown in the summer sun!

You'll also want to be circumspect on the variety of tomato to grow under fluorescents, since it will be necessary to keep the light very close to the leaves for them to grow adequately. My favorite for growing under lights is Red Robin. It never gets more than a foot tall and produced well for me under lights last winter.

I also grew some Cubanelle and Jimmy Nardello peppers this way.