When adding a new post & clicking "post", it processes slowly because the links are checked for malware & bad URLs are rejected. Also thumbs are generated. It does not (yet) create Peachy galleries. You mean that operation? Yes, it's a bit slow nowadays, only a new server will help...
When the links are clicked, the new peachy galleries are created on a seperate server. This will help to preserve the gallery, even if the original server link will go down. If the original server is up and it's too difficult to create a peachy gallery, we'll only be redirected to the original one.