The recommended bandwidth for Dragon Medical is 1.3 megabits up. The central processing method is the same that AC uses. So if you don't have a good enough internet connection going to the cloud, you'll have the same issues. The worse the connection, the more compression has to take place. This will make lower quality mics stand out even more.
Now if you're having that issue in the office, there's likely a problem with your WiFi. In the office, you should have more than enough bandwidth to run Dragon Medical over RDP.