What would happen if I changed my startup disk to a flash drive, then tried to turn on the computer without said flash drive plugged in?
The main reason for selecting a startup disk in System Preferences > Startup Disk is to let macOS know where it should boot from by default. This does not prevent macOS from booting off another drive in the event there is a problem with the default drive.

So, in the event that the default drive is not present or functioning correctly, and there is another bootable disk connected to the Mac (either internally or externally), it should eventually find it and boot off that. 

When I say eventually I don't mean hours, it's usually no more than a couple of minutes.

If there is no other bootable drive, your Mac will display an error, usually in the form of a folder image with a question mark on it.

Firmware password

Note, if you have set a firmware password on your Mac, the behaviour will be different to what I've described above.

If you have a firmware password enabled and you try to start up from another drive (incl. from Recovery), your Mac will pause the startup sequence and present the user with a password field instead. In this case, before the Mac boots up from the other bootable drive it has located, the user will need to enter the firmware password.