No, not quite. The electron-positron collision will allow more precise measurements. The goal is precision, not higher energy range, where a proton-proton machine would be much better. The goal is not to go beyond LHC in energy to see if something new shows up because of moar energy. The goal is to go to high energy with electron/positrons to measure stuff more precisely.
The FCC-ee is an intermediate goal, which will probe similar collisions as the LHC but at higher precisions. It is also a direct successor as the LEP which was housed in the LHC tunnel, so in this sense it is very much about "moar energy" than the previous electron-positron collider that CERN had. They're also hoping against hope that maybe they'll identify some rare collisions and even dark matter at the energy ranges that they couldn't probe before (at the LEP) with such high precision (at the LHC).
Then, when the tech for it is ready, the FCC-ee will be replaced by the FCC-hh, which is the successor of the LHC and can probe energy levels that are completely unaccessible at the moment - at about 5-6 times the energy level of the LHC. This is the true goal of the FCC project, and the biggest reason for building such a huge tunnel in the first place. But this requires significant advancements in magnets and other components which won't be available for several decades. So, they're filling in that time with the FCC-ee.
