Your analysis of the M8 and a GTX 770 is accurate, given all their specs. If the PSU is a dual rail design, that will be worse than a single rail design in this situation.
You read this, but I'll include it here from the M8's specs:
Max. Supported VGA Dimension: 290mm x 137mm x 43.5mm; Max. Supported TDP: 200W.
If you use a graphics card with over 200W TDP, please note that the system’s power supply is only 450W.
A 770 or 780 will no doubt basically work in this PC (if it fits physically), as in boot up, run a browser and do typical PC tasks.
The PSU limit becomes a problem when gaming, when the video card is truly stressed. If (when) the demands of the game such as the settings you use for it, the display resolution, etc, plus whatever else is using power in the PC (mainly the CPU) exceeds the power output of the PSU, then problems will occur.
Best case situation, the PC will just restart. No one can guarantee that this will always happen. At that time the PSU will be hot and stressed to its limit.
If the PSU's over power protection is not good, it could be damaged. Other parts of the PC could be damaged too if the PSU fails.
PCs like this are designed for a certain physical size PSU, meaning you can't replace it easily. The case uses four 70mm fans for cooling, which are small and won't move much air. Heat will be a problem when gaming with a 780 in this PC.
Bottom line, using a 780 in it will be a gamble. The PSU is definitely to small for most gaming with a 780. The M8 is not designed for use with high end video cards.