Even better connectify always setup your NIC as AP and client mode regardless if it can connect or not to your home router. You need to setup connectify this way cause it is not the default behavior. So you can always connect to your haedless box directly accessing it as AP. If the headless box is connected to the internet it will provide internet access to the connected clients, you can also connect to the headless box using its connection to your home router (or from the internet teamviewer)
You can set an static IP address to the AP interface, so you always know how to access the box. When I am at home I access my headless box via my regular router cause my observatory is in my backyard and the signal of the headless box is weak. However when I am in the observatory I connect to the box directly using it as AP, then the box will route me to the internet. In the field I connect to the box in the same way however since there is no internet I can only use teamviewer with the fix IP address of the AP interface.
It is like having 2 nics, one set up as AP and the other as client.
Regarding the headless hdmi dongle, well I had some issues with power management, for instance the PC suddenly went to sleep for no apparent reason despite the fact that I tuned off all the battery save options and explicitly set it to always be on. But I must admit that I never tried RDP, probably RDP will keep the box awake. As soon as I added the HDMI dongle all the power management issues went away. Probably a bios issue, go figure.
Cheers,
Jose