If you measured the salt in your pool, you'd find plenty. You probably already have a salt water pool! All chlorine-sanitized pools are salt water pools eventually. Chlorine, pool acid, and people all leave salt behind when they are done with what they do in your pool, and that salt doesn't evaporate. It builds up just like your CYA does.
And with almost no exceptions, the level of salt in an SWG pool is not corrosive to anything you might have in or near your pool. The "bleach pump" is also going to leave salt in your pool, so that is not a solution to ridding your pool of salt.
Add to that: where once the cost of running an SWG pool was pretty close to running a liquid chlorine pool, since the rise of liquid chlorine costs that is no longer true. It's considerably cheaper to run an SWG.
Add to that: a "bleach pump" still requires you to buy, lug and store the chlorine. And that chlorine, sitting in a big tank outside somewhere, is going to be even more prone to losing its effectiveness (bleach poops out from age and UV), which makes running a bleach pump even more expensive.
AND! If you're willing to invest in a "bleach pump," you could put that to an SWG instead! The cost of running a liquid chlorine pool, just using jugs manually, is already more expensive than running an SWG pool, and you're considering piling on to that the cost of the chlorine pump equipment!!
If you want to solve the liquid chlorine "issues," and draining due to CYA issues, you should be looking at SWG, not bleach pump. IMO...