rich 49 wrote:
Would this (shutting down packs) provide a little more power on the remaining engine?
The answer to your question is definetly yes. When you bleed your engine to power the pack, you are taking energy from it.
Just to give another example (besides that ones our friends already gave), when you have an engine failure on the 737-200, on the "1 eng inop ldg checklist" there's one step where you can configure your acft to become "APU bleed", in order to have extra power to an eventual go-around procedure.
Cheers,
PP