Certainly, vegetables can be grown indoors under lights.
Most appreciate full sun. Generally I recommend 400w CMH.
With the appropriate reflector, such a light can cover
about 3' x 5' up to about 2' tall.

Lermer: Can tomatoes of any size be grown--say at least 6 ounzes? If so, what lighting would you recommend for a 12' X 12' area with twelve plants growing horizontelly?

On a TV show they said you can use regular florescent bulbs instead of buying expensive grow lights. If so, do they work as well for growing basil or tomatoes inside?

of course.
LED grow lights now also can be applied for veggies.
It can be used as light source, thus contributing to the growth of veggies in greenhouses or indoor gardens and to increase their production.

i am attempting peppers and tomatoes - will run MH 800 W x 2 plus HPS 600 W x 1 for a 4 x 9 foot area. I think this might be too much light, but better than too little. I have a 4 x 4 foot propagation garden with 7 x 2 shoplight T8 overdriven, total 14 lamps, 4500 lumen per square foot. This fluorescent garden could even grow short pepper plants or short totatoes.