That's exactly what it does. I have no monitors hooked up to my server yet I use it as 5760x1080 through RDP. The desktop adjusts to the resolution of your computer. LMI is also capable of changing the resolution but it doesn't work as well as RDP. Also a lot of the pro features of LMI are standard on RDP. VNC/LMI are "dumb" protocols in the sense they just update the screen. RDP is an "aware" protcol which knows only to update certain regions that are being used. It's more efficient than LMI.
Sounds intriguing if it both "feels faster" and solves the resolution issue. But do we need VPN for this? Because you say "open port 3389" which is fine, I can do that. But how is it I connect to one of my machines? The router just has one static IP facing outwards -- but somehow I need to remote into specific machines. This is what LMI does, gives you an external URL to go to and see a list of your machines, isn't that solving the NAT problem? We have 10 PCs in the office and 3 providers who log in remotely with LMI.