simmerit No, this only applies to Pets, not the other expansions. I believe that EA added the shop to everyone's accounts (once they own Pets) due to some issues with people getting it in the first place, but that was a long time ago.
On the other hand, many players get Barnacle Bay for free due to a problem with Island Paradise-related content, even if they bought IP years after the fact (and that includes me). So you might find you have a free world, and it might be true even if you never buy IP, so check the product page to see whether you can download BB right now, and if not, again if and when you buy IP.
https://store.thesims3.com/barnacleBay.html?categoryId=12642