Does the bolt peep sight use the same height front sight that is used with the rear barrel open sight?

Simple answer is NO.
The shooter using the barrel rear sight sometimes has the front bead sit low in the notch, but typical peep sight aiming places the front bead centered in the peep aperture hole.
The difference may be small, depending of your particular configuration. Difference depending on your aiming may even be almost undetectable.
Also, the receiver bridge may not allow the aperture to go low enough to use the existing front sight. If it does go low enough, then the bottom of the barrel rear sight may be blocking the lower half of the peep sight picture.

Jim and Bob,
Sorry but the Win. mod 71 does use the same height front sight or at least the ones I owned did. It was designed to do so from a production standpoint. If you install a Redfield or Williams for instance then this would not necessarily apply. It only applies to the Win. installed bolt peep.