Check your available power and rotation rate using the formula on page 9 of Hugh Piggott's handy guide...
I recommend doing this in a spreadsheet for several different windspeeds.
(1) The blade design you chose determines your tip speed ratio. That gives you the rotation rate at any given windspeed.
(1a) Blade diameter and windspeed give the available power.
(2) The Kv (speed constant) of your chosen motor will then tell you the unloaded voltage at that speed.
(3) The available power divided by that voltage gives you the maximum current you can expect.
(4) Now multiply the motor resistance by that current : this voltage is lost as heat inside the motor. (NOTE: Kv and winding resistance will be specified for any motor worth buying.)
(5) Subtract the voltage loss (4) from the unloaded voltage (2) to get the expected output voltage.
(6) Divide output voltage (5) by output current (3) to give the ideal load resistance. Note that this resistance is different at different windspeeds. Too high a load resistance extracts less power than is available. Too low tries to extract too much, which will stall the blades.
In a battery charging application, the charge controller could use something like a MPPT (Maximum Power Point Tracking) algorithm to regulate the charging current, to find the best load impedance to place on the generator. Or simply adjust charging power to match the windspeed. I have no idea if your chosen charge controller does this, perhaps its datasheet can answer that.
(7) Multiply output voltage (5) by output current (3) to give the expected power output.
If power output (7) is bigger than the motor's rated power you need a bigger motor. If power output (7) is much smaller than the motor's rated power, beware : too big a DC motor may have too much friction to turn at all at low windspeeds, and will waste power at any windspeed.
You can eliminate brush friction (but not cogging or bearing friction) by using a BLDC model aircraft motor. This generates 3-phase AC so you need a rectifier to get DC. Having an oversized BLDC motor is not a problem and usually helps efficiency by reducing the winding resistance (step 4) - the remaining downsize is cost. If that's an issue, details on building your own here...
(You can eliminate cogging losses too, by building a custom ironless generator, which is what Hugh's book above is about).
Many more resources on Hugh Piggott's website http://www.scoraigwind.com/
Now to the actual question : is it viable?
Knowing the overall project cost, the likely generated output, and the price of getting that power elsewhere, you can work out the payback time :-)
But the real value (unless your city derives all its electric power from AA cells!) is learning and experience.
Best Answer
You stated your battery is 12V 7Ah battery.
LED (actually the bar light uses 4) is 12-14V (that's the drop), and they say can use up to 10W. Let's do the math: $$ I = \frac{P}{E} = \frac{10W}{12V} = 833 mA \\ $$
No sense in calculating at 14V, you're limited to 12V.
$$ 3 \cdot 0.833A = 2.499A $$
So, BEST case, 2.8 hours. But you really need to see the curve for your specific battery, and it's derating for thermal, etc, to see if it can realistically output 7Ah-- manufacturers (for marketing purposes) usually put the 'best case' information on the battery, but only the datasheet for it will provide the truth.
I'd expect 2 hours and change. If you put an ammeter on it when you get it, and see how much current it's actually drawing, that will let you get a better idea.