Yes. If you say like that, everybody will understand what you're gonna say. Anyway the better translation for that is "네가 그랬다고 인정해!"

그랬다 is basically short for 그것을 했다. But nowadays 그랬다 is quite more spoken and even almost all Korean people think that a man is weird if the one said 그것을 했다. So, generally nobody says "네가 그것을 했니?". We say "네가 그랬니?" instead. In a nut shell, '그랬다' has the meaning of 'did it'.