I've generally had success cooking dried beans in a slow cooker for about 5 hours on high with plenty of water (about 4 c. per 1 lb of beans). While you COULD add everything at once, I wouldn't recommend it, as the rest of your vegetables will become mushy and grainy.
For that exact recipe, I'd cook the beans in the slow cooker, than combine everything on the stovetop for about 45 minutes to get the flavors to combine.
Poaching is about cooking something gently, until just done. This is good for chicken breasts: white meat has very little fat and connective tissue, which makes it well-suited to this. It's at its most tender when it's not overcooked. Dark meat will be fine too. As with most other methods of cooking, it just needs to reach the appropriate temperature in the center.
Slow cooking, on the other hand, is about bringing something up to temperature and cooking it there for a long period of time. (There's no temperature to reach - it'll have been hot enough for a long while.) With meat, this is good for tougher cuts, as the long cooking helps break down connective tissue and soften it up. This is amazing for something like a pork shoulder, which can be cooked for hours and hours, until it's completely falling apart. You can probably get some fraction of that effect with dark meat. White meat will be iffy.
As for your favorite topic, salt absorption, longer cooking will get you more penetration into the meat, especially if it begins to fall apart. That won't happen easily with white meat, though, so it'll be a small effect - possibly you could cook it a while then pull it apart with a fork to help. It'll be a bit better for for dark meat.
Finally, since you've posted so many questions asking basically the same thing, my two cents: the best thing to do is probably just to roast chicken (don't overcook it!), shred it, and add some kind of sauce with a decent amount of salt. Cook it a little bit longer if you like, and there you are. You can only go so far with boiling/simmering/poaching/slow cooking, no matter how much you try to optimize it, and you've already gotten the main advice in other questions: possibly tenderize it, cook it in salty liquid, and perhaps help pull it apart once it's mostly cooked.
Best Answer
Yes, you are slow-cooking correctly. If you were cooking some
chicken adobothen having the meat fall off the bone is intended.Otherwise if you want to serve if while everything is still attached, you can do so anytime after you have simmered or poached the chicken (making it safe to eat), not sure it qualifies as slow cooking however. As pointed out by @Aaronut, extended cooking will break down connective tissues - it breaks down collagen.
Here is some information about searing; it can cause a maillard reaction which does a few interesting things:
In some cases, pressure-cooking can achieve the same results as slow-cooking in less time, while making it easier for the maillard reaction to happen.