I'm just going to lay out my assumptions, or what I think I know, so that there's a better context for the question.
I understand that there are basically four main situations in which a standard lead acid car battery will not be able to hold a charge, the first two being related and permanent:
If the battery is charged too rapidly, water may be decomposed to form H2 and O2. ... The evolution of these gases can dislodge lead, lead oxide and lead sulfate from the plates. Solids accumulate as a sludge at the bottom of the battery. In time they may form a short circuit that renders the cell useless. Chemistry The central science 2nd Ed. 1981 pg. 571
So basically rapid charging such as what happens when the battery is drained overnight, jump started and recharged by the alternator, causes cavitation damage similar to what happens in a cooling system, reducing the effective surface area of the plates and thus permanently decreasing the battery's ability to hold a charge. In fact, according to what I've read 58% of battery failures are due to overcharging.
This kind of rapid charging or overcharging also causes loss of water from the cells via boiling, however this can be fixed in some batteries by adding distilled water back into the battery. This is the third type of damage I'm aware of.
However, there is fourth type of damage, potentially reversible, called sulfation:
When a battery will not accept a charge, it is probably sulfated. This happens when the battery is allowed to remain in a discharged state. The lead sulfate in the battery plates becomes hard and resistant to recharging. ...During charging, the lead sulfate is supposed to decompose into lead, sulfuric acid and lead oxide. However, this decomposition is never 100% due to lead sulfate's insolubility. This means that over time less and less surface area of the electrode plates is available for recharging the battery. Automotive Service, 3rd Ed. pg. 384-385
Now to the question about battery conductance testing:
Conductance testing gives an indication of the amount of battery plate surface available to react chemically with the electrolyte and produce current. Automotive Service, 3rd Ed. pg. 387
So my question is, can a battery conductance tester tell the difference between the loss of plate surface area due to permanent plate damage in the first case, and between the potentially reversible loss of active surface area due to sulfation?
I understand that there are actually multiple different types of battery conductance technology.