Piltdown Man, FCOM only states the limitation of 15000 feet for running the packs with the APU. Nowhere is written what will actually happen in the situation described by topic starter, i.e. a continued climb to cruise level (say FL380) with the APU supplying both packs.
There was absolutely no need for those harsh words. Do you know what happens to the APU passing 15000 feet? You fly the type, you seem to know it all, so enlighten us.