I don't see any reason you can't do this if certain things are taken into consideration. Obviously you will be growing tropical species, and small specimens at that. Even if you have it in good light the plants will be behind two panes of glass so you will need to provide supplemental lighting.
Also, one of the main ideas in bonsai is thorough drainage so if you were considering planting directly in the aquarium I would reconsider. Pots with drainage holes are a necessity. This implies you would have to remove the pots to water them so you don't get too much water inside the aquarium.
Unless you are growing plants that require high humidity you might find this arrangement cumbersome.