Sort of. The Stories series games are not really meant for custom content - they're meant to run light on laptops, so it's really best not to load them full of custom content.
However, you -can- use basic custom content.
I would not use any hacks, hacked objects, or custom objects of any sort - it's a different game with different coding and I could not predict what would happen if you ran into a conflict or something an object needed that Castaway didn't have.
In addition, I think custom accessories (glasses) do not show up in Castaway. Most clothes apparently do show up (I'm assuming ones on custom meshes, or meshes included in Castaway) and I can confirm personally that default replacement skintones, eyes, eyebrows, and hair textures work as well. I've used just those last types and found that was all I needed. Since Castaway is so wildly different from the actual game, custom content of other types would clash with the style anyway.
Downloads for Castaway are placed in:
My Documents\Electronic Arts\The Sims™ Castaway Stories\Downloads
Yeah actually it does, several mod items from sims 2 can be used in Sims 2 Castaway, but not all. I don't mean things specifically created for a Sims 2 expansion or stuff pack, I mean lets say its a chair, you download it and put it into Sims 2, yeah? But try it in Castaway and it does not. Also some mods may conflict in Castaway just like Sims 2. Its a mater of trial and error, and/or some mods that worked just fine no longer do. If you want to find out whether or not your downloaded content is installed and works properly, like the above says you have to enable it, exit the game after being checked, and reload the game, but also rather than try to figure it out in story-mode, see if it works in free-play mode or the tutorial mode. You have to create a folder named Dowloads just like one for Sims 2. You can also put your own pictures in the paintings folder for when your sim goes at it on the easel, again though if ones don't appear, the blue box with the "X" through it, this is due to the picture is too large, this has nothing to do with any type of error.