Let's talk about distilled water.

The water that comes out of a dehumidifier or air conditioner -- like all water condensed from vapor -- is distilled water. Now, I have seen in the health food literature that one should not drink distilled water, because it will leach minerals from the body through osmosis; but I can't figure out the logic there, because it seems to me that when I metabolize that water, the minerals it took from me would be put right back.

Rain water is distilled water -- it is condensed from vapor. As I understand it, the reason it doesn't leach minerals out of plants is that in the process of percolating down through the soil, it gets remineralized by the time it reaches the roots. So -- following my train of thought here -- it should be okay to water plants with the water from an air conditioner, because it would pick up minerals in the process of percolating down through the soil.

Am I on the right track, or have I omitted something?

I think you're fine there, as a totally unscientific study I can say that my house plants have been fine for years with dehumidifier water as we have hard water here and I don't want to give them that. (silica gel dehumidifier)

I remember learning thre science behind why distilled water leaches minerals in college, but that was ages ago. It does do it though. If your mineral intake is high enough, then your body will compensate, but if you have been sweating a lot and thirsty, where are your salts? That said, rain water is not distilled water. The water molecules are organized around a seed of usually something not water, so if you look at a bucket after it rained in there you'll see dirt. It also picks up stuff as it falls.  Water sticks to stuff. The molecules are polar. That said, if you are throwing distilled water on your plants and your soils have enough mineral content or are even too salty, it's fine,  in my humble opinion.  If your soils are low in minerals you've got other problems which can be exacerbated by large quantities of distilled water.  I have used distilled water on house plants that had mineral build up.

There is a lot of weird theory out there about water.
Obviously, with distilled water you are not getting trace minerals and elements you need, and they need to come from somewhere.
But more importantly, body processes need these traces for normal function. For example, to excrete urine the body needs to send it out with sodium, and if it`s not in the water the body takes it from other places. And when you start altering your potassium, magnesium, calcium and sodium levels all sorts of systems are effected, most notably cardiac but the whole machine depends on them. There has been a lot of research done on this by WHO as countries are increasingly looking to desalination. Generally some sort of mineral content is added back in since long-term effects can be very serious.
I think your plants are fine, since any water, even distilled water, is mixing with soil immediately. The air conditioner is condensing room air plus whatever is in it, not distilling and separating, and so whatever is in that air (all sorts of stuff) is going into that condensed water. Probably the biggest risk is to you, on the off chance that some sort of nasty mold is growing in the water and you have an immune deficiency. (full disclosure: I water my plants with the water from my dehumidifier)