This will be possible, with one catch: if you're trying to move forward from B/W to X/Y, that requires two programs: Pokemon Bank as well as Poke Transporter. Currently, the only way you can download Poke Transporter is by opening up Bank while you have a paid subscription, then selecting the menu item to take you to the special page to "order" Transporter as a free download from the eShop.
When Bank turns free, that will be concurrent with the 3DS eShop "shutting down", which means that if your account has already ordered some titles, you can still request to redownload them from the server, but you won't be able to get any new ones. We don't yet know whether the situation around Poke Transporter will count as a new download, or a redownload of something you already have access to. It may end up being the case that you'll be forever locked out of Transporter unless you already downloaded it from a time when you had an active, paid subscription, if transferring up from B/W (or the GB games) is something you want to do.
Moving from XY to Ultra Moon is completely unaffected by Transporter, so at least that interaction will be guaranteed to go smoothly using just Bank after it becomes free.