How would the wave drag of an elongated Sears–Haack body change with a cylindrical mid section?
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.