Ivan Webb Servicing Profiles is client-driven, so the service waits for the device to check in. So, there is no way to accelerate the update from the service side. But, we are currently rolling out two changes which address your scenario:
- We reduce the number of check-ins required for a device to start performing the actual update. This should shorten to time between devices are coming back online and the actual update starts.
- The "update now" button in the backstage of the apps (File > Account > Update Options) will no longer be disabled when a device is managed by profiles and the user can trigger an update on their own.
Both changes are in the process of rolling out this month/next month and should help with your scenario.