No. Remote Desktop client is meant to be used to connect to different servers, so connection information if stored, is stored for that server.
But I have the next best thing!!
Microsoft released a program called Remote Desktop Connection Manager
This is a program that basically does Remote Desktop the same way as the Remote Desktop Client, but instead its designed to handle many different connections at the same time. As a result, you can add a server group, and set global settings that work for the entire group. Alongside of things like resolution, you can also store one or more credentials for that group. If you doubleclick the server, it will connect using the default login credentials. If you right-click and choose connect as... you can use different credentials, and you can save them too, so you can easily connect to various servers using 2 or more prestored credentials.
Have a new server? Add it to the group, and it instantly gets the properties from the group.
You do not really need to work with groups. You can do the same for everything in the settings file, but I recommend using groups. That way, you can have 2 groups with different settings. If you add servers to the main settings file, you can no longer add groups. (learned that by mistake)
