[C650CPT]

Here is my favorite Aviation answer : It just depends.

On our Citation 650 we will use the APU for normal preflight checks ( electrical and hydraulic ) and for getting the avioncs up and running. If it is hot or cold it also supplies us with enviromental air as appropriate. If it really hot we leave it on for takeoff and initial climb as it really helps cool the airplane, plus we can then depart with the engine bleeds off which gives better hot/high performance. If I am departing in low IFR conditions, since it is already running I am inclined to leave it on for the redunancy of electrical supply should it be needed. In a "normal" engine failure you may not loose the other bus ... depends on the design of the system. Most are tied together with bus tie or current limiters, you would need both a failure of a power supply and a same side current limiter before you would notice a bus problem.