So, I already own Din's Curse on GG. If I buy the expansion on GOG, will I be able to download and apply the installer as normal?

You won't even be able to buy the expansion here if you don't already own (or purchase at the same time) the base game here -- the one exception being if you buy it as a gift code...but, even if you did, and sent the gift e-mail to yourself, I don't know if you'd be able to redeem the game with your account without owning the base game. EDIT (for posterity): You would not.

Even if you did figure out some arcane way, though, there'd be no way to know if it'd work except by trying it -- and if it wasn't compatible with your non-GOG base game, you'd be out the money, as they obviously don't support games bought elsewhere, and can't guarantee that the GOG-made installers for the DLC would work with them.