To add to Ian’s comments,
AMR HR will not reduce the RF footprint of your cell. In the worst case, due to weak interference robustness, a MS using AMR HR will have bad VQ and perform a HO to AMR FR, to regain good VQ.
If you force 100% of MS to use AMR HR all the time, without possibility to use AMR FR to fight interference, then you might get some MS with bad voice quality or even call drops.
To prevent this, you must get a clean frequency planning.
There is no “power” reduction due to AMR HR.