Is there any actual benefit to this? Will using one have a noticeable impact on either the individual lifespan of the shrimp, or the long-term survival of the ecosystem?
It depends entirely on your current method of aerating your tank.
If you aren't adding oxygen to the water (usually by bubbling air through it) then the answer to both questions is yes - any aeration is better than none.
If you are already aerating your tank enough to meet their needs, then there's no additional benefit to using this method, other than ease of use if that compares more favorably to your current method.
Brine shrimp (Sea MonkeysTM) survive in low level oxygen environments. They can live long lives with low oxygen levels, so if your only concern is making sure they live a long time, then as long as they aren't dying, it's very likely that you are putting enough oxygen into their environment.
It only takes a few seconds a day with a straw for a human to blow enough bubbles in their water to sufficiently oxygenate the water for survival.
To reproduce, though, they will require more oxygen than mere survival requirements dictate:
...with a good oxygen supply, the brine shrimp are a pale pink or yellow, or if they are heavily feeding on microalgae they will look green in color. In this ideal condition, growth and reproduction is rapid, and a self-sustaining supply is possible. (source)
So by observing the color of the shrimp, you should be able to deduce whether you are oxygenating enough for reproduction or not. Note, however, that reproduction requires several other good tank conditions, so even if you don't plan on having them reproduce, color is a decent indicator of oxygenation.
Typically you don't want too much oxygen - not because it'll hurt the shrimp, but to prevent algae and other undesirable life in the tank. One of the reasons brine shrimp are so popular is because they are easy to take care of, and one of the reasons this is the case is because they do well in low oxygen level environments which acts as a deterrent to other life.