BD's right,

These extra tools to supposedly make your life simpler can make it much harder.
An in-line chlorinator CAN be used with the B-B-B system but the key to B-B-B is regular testing and that won't change. In-lines use Tri-Chlor stabilized tablets and these add stabilizer (Cyanuric Acid, aka, CYA) to your water at 60% of the rate they add chlorine. That's good when you don't have any CYA, but bad when you have enough, and worse when you have MORE than enough. They also add acid, lots of it, so you'll find you'll need to add Borax constantly to raise pH levels. Still, early in the season, an in-line can help bring your CYA level up while maintaining a constant flow of chlorine. In the spring, I usually use the tablets in a floater to achieve the same goal, and watch the pH.

Caveat: Do NOT drive yourself crazy using "Dual Acting" tablets, or ones that say "With Algaecide!". Chlorine IS an algaecide and they are adding copper, which you don't want.

Chlorine reducing systems like Nature2 cost more to use than they save in chlorine. Never trust pool chemicals that don't say what they contain but use cute labels and vague references. Bleach is still the best chlorine and algaecide.

(Note: Many pool stores sell Liquid Chlorine, frequently as "Liquid Shock". If it's 12.5% sodium Hypochlorite, it's nothing more than double-strength bleach--my preferred chlorine. If it's price per unit is less than double the unit price of bleach, it's a better deal than bleach because you use half as much. If it's more expensive than double the price of bleach, bleach is cheaper.)

Carl