While this technique has been taught for decades by some CFIIs, I strongly recommend against it. Prepare (brief) and set-up the approach you intend to fly, and fly THAT approach. If, at some point, it becomes impossible to fly the approach you prepared and set-up for, then execute a missed approach and find a safe corner of the sky where you can sort things out. A LOC is a different approach from an ILS even though they share the same lateral guidance, and any attempt to revert to non-precision procedures and mins while inside the FAF, especially in challenging circumstances, is to invite undesired outcomes.
G/S failures on approach are very rare, but human failures are not: don’t needlessly create another opportunity to bust your ass by trying to switch horses at full gallop.