If you are force carbonating, skip the priming sugar.
I have no experience with Tap-A-Draft, but from what I understand, it's better to naturally carbonate. Supposedly, those little CO2 cartridges go empty REALLY fast when force carbonating.
I've read that they just flat out won't carbonate at all with such small charges. I've read this in a couple different sources. It might be possible with a few liters of beer at a time, but for 5 gallons it'd be impractical.
From some quick chemistry math (My chem honors teacher, who flunked me, would be proud of me right now), let's see here. From my quick research, at 80 degrees F, 1 pound of CO2 takes up about 10 cubic feet (all of this is rounded grossly).
There are 957 fluid ounces in a cubic foot, so 1 pound of liquid CO2 translates to around 9570 fluid ounces of volume at 80 degrees.
There are 640 ounces in 5 gallons.
There is roughly 454 grams per pound. We can do some conversions here now, figuring let's say 2.5 volumes of gas for carbonation.
2.5 volumes of gas, at 640 ounces of beer, is 1600 ounces of CO2 in solution.
1600/9570= .167 pounds of CO2 to carb your beer. You'd need 76 grams of CO2, and at 15 grams per charge, you'd need at least 5 of the bulbs to carb your beer. This is already assuming a perfect environment going from 0-fully carbed, and your container already at sufficient pressure to carb. I'd guess it'd probably take closer to 10 bulbs to do the job though, due to various factors. Part of force carbing is to maintain high pressure in the bottle for long enough to force the CO2 into your beer, and with the bulbs, you might not have consistent enough pressure. The tap-a-draft system might work differently though than those injectors, I wouldn't know.
Wow, that was fun to do all that math, even if it was 3:30am. If my premise is far off, forgive me.
