Hi.
As Cryptomator desktop does not the sync to the online Storage, it will work independently from your Internet Connection. And it does not monitor your internet connection, because it does not use it.
The sync is done by the sync client from google.
If more than one person is working with the files, this post about conflict management might be interesting.
If you plan to use Cryptomator in a business environment, this might be interesting as well: https://server.cryptomator.org/en/