I've tried that, but stopping emigration that way also seems to stop infraestructure trading, and when natural growth set your population over your colony's capacity you get unrest (and a negative growth) until your population gets again under the limit. . . and again you have a natural growth which will lead your population over your colony's capacity again
You can set all Source colonies to Stable, and keep your Destination colony as so. It will still require infrastructure imports while not receiving colonists.
Also, you can manipulate your civvies by making obselete all cryogenic transports, the amount of colonists sent will be lessened compared to infrastructure traded, since all the new ships built will be liners or freighters.
Ah, and luxury liners will send colonists anywhere (source, destination or stable), as long as there's a source to pick them from. Great profit source for you and your civvies.