I don't know about the LM78xx...
Where I work, we sell a board that can be powered by 5V, or with a higher voltage using an on-board LM2741 regulator (similar to an Arduino).
There is a "regulator bypass" jumper that simply shorts-out the 2741 input & output pins for a direct (externally regulated) 5V connection. Sometimes during test, we bypass and "back-power" the regulator (without the shorting-jumper connecting back to the regulator input). With this chip, there is no problem back-powering in either case.
Some of our other products use different (usually switching) regulators (and without the bypass jumper on the board), and when there's a "power supply problem", it's often helpful to temporarily bypass the on-board regulator with a bench supply (to see if there's a 5V to ground short, etc.) and I've never had a problem back-powering the regulator in those cases either.