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Fluorescent lights will keep plants alive, but if you are talking about stock lighting on a tank, the wattage is not enough usually. It really depends on what plants you want to grow and how much wattage you have to work with.
Check out the stickies at the top of the forum. You can grow plants under regular florescent bulbs. Just depends on the wattage and the size of the tank for what kind of plants you can grow.
I have three Amazon swords under 13watts in a 12 litre tank. Also my tank gets a liitle indirect sunlight during the day (I took care not to put the tank by a window though).
Will the plants be getting enough light between the bulb and the sun?
I have enough problem keeping my swords in my 30 gallon long let alone a 3 galloon.
In order for them to be managable you may not want them growing but just maintaining. Not sure how many watts that would take but probably a fine line.