It may increase the duct pressure, and that should increase the air flow through the packs. I don't know whether the amount would be worthwhile.
Not something I ever even thought of doing in the 767/747/380, so I can' say for sure. You might actually be better off restarting the APU and feeding the cabin air from there.
You're not going to increase the power by much, simply because of the jet blast. Perhaps a couple of hundred kilos an hour of fuel flow.
