Hi David-The toolkit deployed for Environments is primarily leveraged during the course of a job... Sync, provision, refresh, VDB disable or enable, etc. As such, the Engine is not terribly sensitive to a period of time that the toolkit is not available unless a job is initiated or in progress at that time.
The Environment refresh is a great idea to ensure the toolkit can be refreshed as expected after the maintenance, and any warnings or issues detected can be addressed at that time. Maintaining correct permissions would be the only immediate concern offhand.
No other DB shutdown is expected or necessary as these would be leveraging NFS storage mounted from the Engine during usual runtime.
Of course, if any issues are encountered please feel free to engage us and we can review as needed. I hope this answers your question!