The only actual problem to be considered, is whether the regulator has a Zener or "shunt" action whereby it will conduct heavily when the voltage on its 5V output rail rises above its reference voltage. Reference to the datasheet reveals no didactic direction on this matter, but the actual circuit of the regulator itself suggests that the "reference" will be drawing some current, but through some resistance rather than "stiff" transistor junctions and that this should be quite safe. In fact, some of the application notes do imply this as well.
The diode from output to input of the regulator is only necessary to protect against a condition where the input capacitors are drained quicker than the output capacitors. If nothing else is connected to the input (and if you are supplying Vcc with regulated 5V, then of course you would have nothing whatsoever connected to Vin), then this has no relevance; the diode is unnecessary.
Supplying regulated 5V while connected to the USB as well is indeed "not considered a good engineering practice", but of course, the protective polyfuse is there and there is no logical reason why this (tending to feed 5V back to the computer's 5V) would cause a problem.