@KoiwiGal - I wouldn't mind the idea of it turning itself off when full though, since I think I would be very expensive for it to be running all the time.
If I was going to do this, I would first make sure I'd done everything possible to reduce moisture in the crawl space. Insulation is a good idea for a lot of reasons and can also help to reduce moisture if you install it properly. You might also want to try and fortify your foundations against moisture by painting them or sealing them. Then, I would figure out the cost of running the dehumidifier and I would get one that could work on a timer so that I could control how often it would turn itself on.
I can definitely see how it would have long term benefits, but you'd really have to see whether the expense of running it all the time was going to stack up against the potential savings from running it. I'm sure in a lot of cases crawl space dehumidifiers are not actually worth it.