Hi K60! Just so I am understanding you, this is what you are proposing.
Mon: PS BACK/BI/ABS
Tues: PS LEGS/ABS
Wed: PS CHEST/SHOULDERS/TRICEPS
THURS: off
Fri: S&H LEGS AND SHOULDERS
SAT: S&H TRI/BI
SUN: S&H BACK CHEST
If you are used to working out with weights regularily, than you could do this all in one week and possibly get some benefits. The reason I say "possibly" is because of the other factors clouding the situation. For instance, you still need time to fit in cardio and now we are looking at 6 to 7 workout days a week plus some days more than one hour of working out per day. This sounds like a set up for overtraining, which in that case would mean NO, there would be no benefits from this weekly rotation. Hope that helps!