I never heard of a "Bleeds-off" takeoff on a -200 before. With 4 independent hydraulic systems powered by engine driven pumps, the bleed air is required to operate the "Air driven pump" in case of engine failure( ADP's are both a supplemental pumps as well as for backup). However, if performance is limiting, there is an easy performance gain for turning packs 1+3 off, closing the isolation valves( now bleeds from eng 1+2 provide air to/ and only to the left wing manifold [ L.E. flaps ], and the right isolation closed and right manifold pressurized with bleed air from eng 3+4. The APU will provide bleed air to #2 pack.
Of course, some freighters have #2 pack removed ( weight loss ), and your APU would have to be operating, as would it's bleed air.
If previous post is correct, about multiple eng. failures, all this performance dialog is moot.