You can do that to create a drip system, but it will be unable to produce a fine mist. Mist requires pressurized water forced through a fine nozzle. Pressurizing water in that way, for small scale hobby purposes, generally requires a diaphragm pump like what MistKing sells (or a RO booster pump, for example). Drip systems can work well for watering plants like orchids hanging on porous media, but I don't think they're ideal for general frog purposes.
Also, if the system was truly air tight, the depressurization of the air space above the water would eventually overcome the pump's ability to move water, in effect continually increasing the effective head height the pump is working against as the water level inside drops. Plumbing is fun!