Fufanu, littlefishie has some good advice there. Depending on what I'm breeding, all of my fry tanks have either air powered corner filters or sponge filters. If the filter on your 20 gal is a power filter, I don't think I would use that on a fry tank. The little fellers just get sucked up into the filter, they're not strong enough yet for that strength filtration.
Actually, to answer your question, you don't technically have to have a filter, but a filter will provide a more "stable" environment for your fry in the long run. If you had no other commitments than to make sure the water was changed on a regular, frequent basis, and could guarantee you would not slip up and forget a few or accidentally overfeed one day, then you could probably get by without a filter. But very few of us can do this, and a filter is just good "insurance".