I'm thinking about buying the game for playing Multipalyer with friends. Since my friends will probably buy it on Steam but I prefer Gog, I was wondering if the two versions can play together without problems? Did anybody try it?

No Problem, same as with Terraria. Since its Working on Stand alone Servers, its Working.
Even on Singleplayer.
It has its own Server Management, thats why its working ;)

Edit : whoops, ah for Singleplayer you have to be in a Hamachi or Tunngle Network.
Seems like Multiplayer also got that prob. But its working over "Join via IP" over the Options
Just type in the Hamachi or Tunngle IP. over Multiplayer.

You could also get a standalone Server. maybe you should tick the option for Validate Game versions, because it can cause problems between those 2 Games. I got problem at least with one steam user wanted to join me, so you have to go to the options and click "Allow Assets Mismatch" if the Error occurs.

@Faenwulf: here is a list of servers: https://starbound-servers.net/

If I add the game on Steam, can I play with friends via Steam?

You should ask Steam forums for that.