Can I use VNC to control RDP sessions on Windows?
No.
Neither TightVNC nor UltraVNC can use RDP, as per this comparison chart from Wikipedia. Sort on the second column ('Protocols') of the first chart to see the apps which do use RDP.
Seems to be possible, but the vnc-server process must start as user-process and not as service. Then use hostname:# to connect, where # is the display/session nr.
Reinstall TightVNC without the start TightVNC as system service option, and put tvnserver.exe shortcut inside C:\ProgramData\Microsoft\Windows\Start Menu\Programs\StartUp