How would the wave drag of an elongated Sears–Haack body change with a cylindrical mid section? Would a Sears–Haack body have the same wave drag as the same body with cylinder of the same diameter placed in the middle, between two halves of the Sears–Haack?
No it will not have the same wave drag.

The low wave-drag of a Sears-Haack-Body is achieved by the smoothness of the body. This means kinks are not allowed. The picture below shows the Mach-Number distribution around a Sears-Haack-Body (taken from YAMAZAKI 2014). Notice the gradual change of the Mach number along the body surface .



The following illustration shows the proposed elongation of the body by inserting a cylinder.



By adding a cylinder the curvature of the body does not change gradually (smoothly) but stops - stays constant - and starts again.

This will trigger a Prandtl-Meyer-expansion (example below, taken from here) which will distort the smooth flow around the body and thereby increase the wavedrag.