On the 757 the Packs Off take-off is effectively an unpressurised take-off. The procedure is to restore 1 pack after 1st thrust reduction and the 2nd when pressurisation stabilises.
The unpressurised take-off is no big deal, done it several times; as previously stated, the Boeing procedure makes no reference to the APU (in the Packs Off take-off)
Using the APU on take-off gives a performance penalty due to the intake door sticking out in the breeze, and APU to Pack take-off may not be used in Icing conditions.
As far as I know, there is no Bleeds Off procedure for take-off.