I just ran a quick test and found that the Compute Stick does indeed boot up just fine when NOT plugged into an HDMI port. And then I tested a remote connection to it with the Teamviewer remote app. Teamviewer found it and was able to remotely control it just fine, with the caveat that the Compute Stick did not use a password to get into Windows. If there was a password, it stopped dead at that point and Teamviewer would not work (as expected).
In regards to USB power - we know this: There MAY be enough power on the USB port to power the Compute Stick. A USB 2.0 port normally only supplies 2.5W of power. The Compute Stick is designed to use up to 10W of power. If the USB port can supply enough power the Compute Stick can be powered. I have not yet tested this configuration.
To boot Ubuntu in text mode rather than with a GUI you only need to change GRUB's configuration file. Edit the file '/etc/default/grub' and change the line that starts 'GRUB_CMDLINE_LINUX_DEFAULT=' to 'GRUB_CMDLINE_LINUX_DEFAULT="quiet text". As you will be booting effectively as a headless server then it also makes sense to change any timeouts to zero. Therefore set both 'GRUB_HIDDEN_TIMEOUT=' and 'GRUB_TIMEOUT=' to '0'. Additionally set the default boot option to match the appropriate menu option noting that zero represents the first selection. You modified file should then look similar in part to:
Finally as root run the command 'update-grub2' to effect the changes.
And if having logged in on the console you find you want to start your default GUI, then simply run 'service lightdm start' as root.