yep the VP44 does not run if the engine is not running (atleast in the 8 years of owning a 01, I have never seen that). Its timed off the of front gear train and I doubt that it would run if it is not getting the timing signal (not positive about that though). The LP will run with a key bump for 20-25 seconds.
The VP is a decent injection pump its the LP that craps out and kills the VP because it is lubed/cooled by fuel. The LP goes out and eventually kills the VP from lack of fuel flow, if you do not have a fuel pressure gauge you dont know until its too late. . Happened on my truck at 45k (after 4 total LP failures it was still running but had pretty bad dead pedal) but I have over
60k now with the replacement and with a FASS pump, not a single hiccup.
Most common failure of the VP from what I can tell is the electronics that are on top of the pump die from getting too hot and there are internal failures (cracked diaphram) from lack of fuel. Like any mechanical item there is a certian number that are just **** right out of the box.
Most common symtoms of a dying VP44 are: dead pedal while driveing, code 0216, hard starts with a hot engine, reduced mileage and power and ending with complete failure. I was able to get about 1. 5 years out of my VP after I started getting dead pedal and code 0216 until it became too much of a pain in the rear.
Hope this helps
J-