Does tube testers tell how much life is left for tubes?

In the end, we usually are alerted to the possibility that a tube or tubes are failing by the fact that the our system sounds "off", not as good as usual.  Only then are we motivated to test tubes.  At that point, if any tubes measure low in transconductance, I ditch them in favor of new.  That nearly always results in restoration of SQ.  I own an ancient Hickok 533A, which I can use to test small signal dual triodes only, to include octal based tubes like the 6SN7 and 6SL7, and it is not much good for testing modern very high transconductance triodes like the 5687 group or the 6DJ8 group, because of its current limitations.  I just shoot for an approximation of "good" with those.  The 533A is no good at all for testing the monster 7241 triodes in my power amplifiers, and for that I just go by listening and then measuring the tubes in situ.  The 7241 is a US milspec power triode developed for use in radar installations.  It can easily run on up to 1A plate current, although I do not stress them that much.

I've just came up with an idea how to deal with when to change tubes. Always have spare tube sets ready. Then, if suspicious, change the tubes. If it sounds much better after the change, keep the change. If the difference is subtle, put the old tubes back and keep listening until feeling suspicious again.

6dj8 6922 types, in my experience, get noisy with tube ’rush’ or hiss, and microphonic long before they quit entirely - not sure why this happens in the physics occurring inside the tube as time passes -- these will test fine on the tester for gm but then plug em into the linestage or phono stage and they are unlistenable

True.

The Following is a recent report I received on a Early 60's produced Valve.
It covers the Anode and Mutual Conductance.
As can be seen each Valve has a very good reading compafrd to a New Factory Spec Valve , whicch is the 100% readings.
What is not shown is if here is a Cathode  / Heater Leakage that if present can impact on a Valves Function for the worse.
 
  Tested on my uTracer @ 90V -1V

100% is 15mA Ia , 12.5mA/V gm
Valve 1

Section 1 – 17.16mA / 12.37mA/V
Section 2 – 16.13mA / 12.39mA/V

Valve 2

Section 1 – 17.39mA / 11.84mA/V
Section 2 – 18.92mA / 13.16mA/V