[SLEEPING DOGS]Activating both Original and Limited Version.

Yes, you will be able to activate it, but it would be a waste of money, but hey that's up to you.

I got the limited version and it came with the Community Gift Pack, GSP Pack, Police Protection Pack, and the Valve T-Shirt Pack.

don't waste the key, the dlc aren't that interesting give it to a friend instead so another person can actually get the game (or make a GA here).
And certainly don't just torrent the dlc and drop the files in your Sleeping Dogs game directory since that works too. That would be immoral - more immoral than dlc itself.

Here's what's included in the Limited Edition

The Community Gift Pack and the Valve T-Shirt Pack are free and automatically included with any Steam version of Sleeping Dogs, btw.
You would only be getting the GSP Pack and the Police Protection Pack out of it, and those have been very cheap in the past.

I'd definitely say you shouldn't waste the key just for that, especially since it's such an awesome game, but it's your choice.

For what you would be getting it would really be a waste.. maybe trade the key to someone without the game and get something more interesting for yourself.

Totally not worth it. Trade your key for some TF2 keys and buy the missing DLC next time it's on a -75% promo.

Also the dlc itself is not worth it (even though I have it) - just some shirts, and there are nicer ones on the game anyway.

Yes you would be able to do so. I know because I did the same. I've been given a free key of Sleeping Dogs but it was a RU version (missing my language). Then I bought the Limited Edition when it was 1.50€ on some website. Now I have Sleeping Dogs + Limited Edition DLCs + all languages (EU + RU).