Virtually There,
I reckon you get the prize for deducing the correct answer. Congratulations! This was the winning statement:
You won't see this extra power with the inertial separator engaged, so if you don't touch the power lever, then an aircraft in bypass will need more runway.
And, if you are following the 750 AFM (the book) precisely, you won't be touching the power lever. That 3% factor, called for by the book, assumes you are complying with the other things directed by the book for takeoff. Those are:
1. That the takeoff power (64.5 psi Tq, 2006 Np) is set prior to brakes release. (Note that you will almost always be able to achieve this power setting. If the separator is open, that will merely mean a slightly higher ITT and Ng).
2. That the power lever is not touched after brakes release. This means that, during the roll, the ram effect will cause the torque to increase beyond 64.5 psi. This does not mean the engine is being over-torqued.
With the separator open, however, the ram effect is not as pronounced. The result is that at rotation time, the power is slightly less than it would have been if the separator was closed.
The power at brakes release is exactly the same in the two cases, due there being no ram effect. It is the change to the power throughout the takeoff roll that gives rise to the different distances.