getochkn :
Yes, it will run fine. It doesn't need external power, therefore your 12v rail is sort of not needed. It draws the power the PCIe slot. This slot by design provides a minimum amount of power.
I hate trying to repeat myself, but there is no external power needed for that card. You're looking at this the wrong way
That is incorrect. The external power connectors are to provide additional power to the card over the 75W that the PCI-e slot can provide, a card can pull about 6A from the 12V rail via the PCI-e slot, the 8400 GS was a 40W or 25W card(2 versions) so it doesn't need an external power connector, but i wouldn't go and replace it with a 7750 that needs 75W but also has no power connector simply on the basis that it has no external power connector.
The R7 240 will use about the same amount of power as the 8400 GS so you will be fine, but it isn't because the PCI-e slot provide a minimal amount of power, it actually provides a rather large amount of power for a peripheral slot.