Every light just about has some of every spectrum, its just higher in certain points. If your T8 says its 2800, it probably is. I do not understand how your lumens are so low? Just one of my lights gives 1400 lumens and its a cheesy 20 actual watt CFL. You WILL need more for flowering even though your trying to keep it down, you gotta beef it up a bit. Or atleast get some stronger CFLs.
I use 2700 kelvin range CFLs the entire grow. Your space is small you may also want to do this. Keep the lights as close as possible to the plants with a light breeze on them so heats never an issue. (My lights sometimes touch the plants in veg stage, never burnt a leaf) Helps avoid stretching and not using the proper spectrum during vegetation will keep the robust growing to a minimum and also keep the plant smaller.
To answer the last question more throughly, no that much light will not be enough to flower, as mentioned above in my post youll need more lights or at the very minimum stronger lights. (I grew 2 plants fairly well with about 12,000 lumens in a armoire but the lights were almost touching the plants and in all the places the buds would be the entire life cycle)
The above poster is correct though, if you want to do it all properly..... 6500 kelvin range or so for vegetation and the robust growth, 2700 kelvin range for flowering to improve bud density and production.
i got some new CFLs 23watts (6500k) today