I found this on the iLok website. This would lead me to believe the deactivating before refreshing the computer would be the prudent move.
Host Computer
Your software might allow activation to your local host computer. This works the same as activation to an iLok USB, but without requiring you to purchase and carry an iLok USB.
Remember, once you activate a license, the license is in that location, not in your account. This means if you lose access to a host computer due to a hardware change, or a lost, broken, or stolen computer, you would lose access to any activations that were on the host computer, just as if you lost your iLok USB.
You should be very careful to deactivate licenses from your host computer back to your account before making major hardware changes or selling your computer, so that you do not lose access to your licenses.
If you do lose access to a host computer activation, you can use iLok License Manager to
report the computer as unusable and request that the software publisher(s) send the licenses back to your account. Reporting a computer as unusable is permanent and irreversible.