If you tune downard tonaly, so from an F# and you want an F, the string will more easily fall out of tune. I am not sure what causes this, some interplay between the friction of the peg and the final resting position of the string on the nut being different depending on the direction maybe. By tuning down perhaps you end up relying on some of the friction from the nut which goes away quickly as the string settles to an equal tension on either side of the nut.
I have noticed it's not as much of an issue on carbon nuts or well made nylon/bone nuts.
The big problem with trying to tune a guitar that way is that you're tuning a guitar so it's in tune when you don't press the strings, but then when you actually play it you do press down the strings. Strings 5 and 6 should be tuned slightly flat relative to the first four, the exact amount depends on your play style, but if you don't tune them a bit flat then they'll sound sharp when you're playing. If you haven't tried this yourself you might guess that it's subtle effect, but depending on your play style it can be huge.
The other problem is that the harmonics are actually 2 cents off of an equal tempered fifth, and if you tune six strings that way you'll end up 10 cents off. Your octaves will sound wrong.
When you press the strings, they will all press equally, playing a correct relative tune.
Hearing loss has no impact on this - unless it's really, really bad, of course.
You can get around that by using harmonics. Because you play harmonics without pushing all the way down, you can achieve a more precise tune.
The strongest harmonic is achieved when you gently place your finger on the string directly over the metal fret. A harmonic can only be achieved when you do not press the string all the way down into the fret.
The harmonic on the 7th fret of one string is the same note as the harmonic on the 5th fret on the next higher string. This is true for all consecutive string pairs other than (G, B).
You can tune using these pairs of harmonics to tune more precisely than pressing all the way down.
You will need to tune the (G, B) pair without harmonics.