Yes, this is an administrative change that should be notified to the DVLA immediately but the driver is allowed to continue to drive on a public road as long as the driving licence categories (on the back of the licence) are valid and in-date.
Although a change of address is administrative, it is important that the driver notifies the DVLA as any penalties or fixed penalty notices for offences that do not result in a disqualification but are issued with penalty points are required to surrender the licence for the points to be added.
Where a driver fails to surrender their licence, DVLA will write to the driver (latest address recorded) requesting the return of the licence to the Agency. DVLA will give drivers 28 days to comply before the licence is revoked.
As an employer, you need to ensure that your drivers are aware of this requirement as any letters sent by the DVLA to an address that the driver no longer resides at could have their licence revoked without their knowledge.