It is possible yes. If you do go ahead with seahorses, i would suggest one of the smaller of the greater seahorses. You could do Redi or erectus, but they are MUCH easier to keep in larger tanks. I would use no less than a 29 gallon for them. However, it is possible to keep a pair of them in a 20 gallon tank.
Some other options that would probably be better:
H. Kuda
H. Whitei
H. capensis (this is a cold water species that would require a chiller)
Best bet would be H. barbori IMO
They are tropical, and only grow to be about 5 inches, yet they still eat frozen mysis. Typically they are hard to find, but Ocean rider (seahorse.com) is now breeding them and they are available, but as allways with oceanrider, they are not cheap.