No. Without a licence registered to that site the updates stop, and the install sits on whatever version it was on when the licence lapsed or was never applied. Agencies find this on sites they built years ago that are still live and still earning, where nobody has looked at the admin in a long time. Buying a licence now gets you current, but it also buys you into the maintenance track. If the site simply needs to keep working and keep ranking, moving the content off is usually cheaper than licensing it and it ends the problem rather than deferring it.
