Yes...with caveats...
Don't add more fish than the media can support, and stay on the consevative side (so, if your mature filter is supporting 30 neons, and you took a third, you would want to add six or eight to the new tank, not the full ten).
Feed very sparingly and test frequently in both tanks for a week or so, in case of mini cycles.
I prefer to qualify mine; I set the tank up, and plant it and add some fish food (because I clone all my filters and don't have ammonia, but ammonia would do too, if you have some left from a fishless cycle). Once I can read some ammonia (it'll only be 0.5 or 1ppm with fish food) I add the mature media last thing at night and test first thing next morning. If the ammonia has gone, I know I'm safe to add fish.