Cheap LIFEP04 batteries

[the evil twin]

Same here Jack.

I've got a dumb question. If I have a device that draws that 20Ah and run it for 6 hours off a 120Ah battery, does that mean the battery will be completely flat after 6 hours? Is it that simple?

Assuming a standard Lead Acid tech battery and if the 20Ah device does not have a low voltage cutout...

It will be "completely" flat well before 6 hours due to other losses.
It will be "effectively" flat after about 3 hours
You will risk damage to the device/cable/ after 2 to 3 hours because as the battery supply voltage falls the device will draw more current IE as the battery voltage falls the current draw will increase proportionally (P = E x I ... where P equal power, E equals voltage and I equals current).
or...
if the device is voltage sensitive it will not operate at best efficiency which is equally likely to damage it.

Edit... Devices are rated in Watts not A/H so whilst the above is not exactly technically correct, I left it as is to avoid confusion.