Yes, you need a Dropbox account to join a shared folder. Files in a shared folder sync between members in their Dropbox accounts, so you need a Dropbox account to access and sync changes.
If you invite someone without a Dropbox account to a shared folder, they will need to create an account to join the folder.
If you don’t have a Dropbox account, you can:
Can I receive shared files when I don’t have a Dropbox account?
You don’t need a Dropbox account to view the files in a shared link, and you can download those files to your computer. Files that you download from a shared link won’t sync with Dropbox if you edit them.
Can I upload files to Dropbox without a Dropbox account?
If someone requests files from you, you don’t need a Dropbox account to upload files into the file request. However, without a file request, you need a Dropbox account to upload and share files.