Your two florescent should pull it off. Of course I am gonna tell you that you should add more light but your question was "will it work"? I say yes. If you are worried about the cost of some real grow lights or gear hit up this link. I get all my gear here and they are the cheapest online hands down. My system paid for itself 1st crop. Good luck hope this helps!
Here is a place for seeds. Google Totally Tomatoes
Get TOTEM they are excellent for what you want to do. I would use LED plant light. I've been using them to start plants for a few years and though pricey the electric bill is cheaper as you need 16 hours of artificial light a day. Also you need to play bee. You have to take a Q-Tip to the flowers to get fruit.
Go to Amazon.com and search for LED Grow Lights In patio and garden.
I don't blame you for not wanting to click on links. I have the 225 bulb square ones.
These look good and are very reasonable and get good reviews.
HQRP 28W 450 LED Blue + Red Plant Grow Light Panels
Tomatoes need temperatures from 80 to 90F. And they need airflow and space between them. The sun ripens the tomatoes.
A slow fan can give airflow.
The lower leaves turn yellow and need to be taken off.
yes you can
do you think that i can grow and fruit a mini tomato plant with one two socket t12 with two 2ft 20 watt fluorescent tubes in it?