Any ideas if the DLC is compatible with the base game I purchased on GamersGate?

It might well be, but you won't be able to purchase the DLC here (or redeem a gift code for it) unless you first own the base game here. Not sure if you can purchase it separately from the developer's site or not. Otherwise, you'll have to either wait for it to go on sale at GG, or get the base game + DLC somewhere else (like here) when it's cheap.

I just register the game and download everything from the main site. Updates come out quicker there than anywhere else after all.

The DLC is one add-on file BTW (as most add-ons are for this game) so if it isn't a yes I'd be worried.

You should be able to buy the DLC from within the game, actually, if you're worried about compatibility. Then it'll install it directly from te4.org, much like addons when you install them from within the in-game browser.

I forgot that it's impossible to buy a DLC without the base game, thanks.

It is very weird that GOG blocks DLC purchase without owning the base game, since in this case the base game is free and open source.

In this case even if it is free, you can't use the DLC without the donation version anyway. So it works like normal DLC does on GOG anyway.