This may be surprising, but no. The client is only required to have an occasional  internet connection (like a guest WIFI anywhere). The reason is, clients will ask the cloud service roughly once a day for current settings. The client then knows your current rules in case the user needs to elevate offline. If you then have auto-approval on, the client will allow the user to become administrator temporarily and will queue the data locally and log what has been done, including date & time, installed applications, exe files run as administrator and so on.

Once the client has an internet connection again, it will flush the queue to the cloud service and all data is uploaded. This means that the client works exactly the same whether online or offline. The only difference is the time the reporting data becomes available in the cloud service.