I'm not concerned about the temperature of the cathodes because the 3.4V are applied when tube is running, so the ion impact adds to the filament heating.
In total, the filament receives enough thermal energy to keep the emitter up and running.
When not lit yet, the voltage is 6V which is good enough to heat the cathodes properly. I've attached a picture of my ATLAS 20W preheat tube on a 6V
heating transformer, you can see that the filament has enough temperature. The other tubes (40W, 65W) are in the same ball park.
The 9V electrodes are constant current type electrodes, they develop a drop of around 9V when run on a conventional ballast in preheat mode (short circuit
current). They are designed to reach emitting temperature when the preheat current is passed through them. The voltage across the filament depends on age
and state of the electrode. The voltage drop of 9V is valid for new filaments with the full emitter available, they tyically develop a voltage drop around
8 to 11 volts, that's why they are classified as '9V' electrodes. Wornout cathodes have a much higher voltage drop, I measured up to 14 volts on T12 and
up to 17 volts on completely blackened T8 lamps. CC electrodes can cross-ionize, drastically reducing their resistance, but that is not a problem when run
on a magnetic ballast.
Rapid start electrodes are constant voltage electrodes, they are designed to reach emitting temperature on 3.6-4 volts. The current through the filament
develops depending on age and state of the cathode. CV electrodes do never cross-ionize, as this had fatal consequences if the voltage source is not
current-limited. However, most heating transformers do not have the best magnetic coupling, so the output current is somehow limited.
If you put a rapid start tube into a preheat fixture, the short circuit current of the magnetic ballast is not high enough to heat the low resistance
filaments up to the correct temperature, so switch start fixtures would have a hard time igniting RS tubes.
Vice versa, if you put a preheat tube into a rapid start fixture, the preheat voltage is not high enough to bring the 9V electrodes up to temperature.
In both cases, the cathodes would run too cold, probably blackening the ends of the tube and paying with service life hours. Besides that, nothing else
would happen.
Actually no, there are 3 seperate type of T12 flourcent tube
those with 8V cathodes are *not* as you describe, they are designed for 8V-10V cathode heating, usually by way of an Autotransformer Quickstart unit after the choke, but also can be applied by way of non-autotransformer cathode heating unit (see US Trigger-start ballasts and British Dimming ballasts)
the current defined type your thinking of are their own standard in itself, and they have no defined cathode voltage or resistance
here is an excerpt from one of my recent comments on the Gallery

TL lamps are switch-start lamps with current-defined preheating electrodes that have no actual set voltage, an MCFE tube will *always* have 8V high resistance cathodes
but a TL lamp will have cathodes of no actual fixed resistance/voltage value, for example a 1980's Dutch made TL 20W/05 Ultraviolet tube I have has cathodes that are somewhat of a medium resistance, but the dutch made MCFE 20W/840 tubes I have are proper 9V high resistance cathodes
a TL lamp is only an 8V lamp if its a TLA type *or* there is a T suffix *after* the colour code, ie TL20W/33T, but I have never actually seen the latter pictured, only mentioned in some catalogs
see page 346 if going by PDF counter or Page 310 by the page number on the catalog itself, for more details
https://www.lamptech.co.uk/Documents/Catalogues/Philips%20-%20Catalogue%20-%201979%20UK.pdfthis is why for a lot of common T12 tube types, there are actually 3 separate types listed in the IEC standards document
for example for the Humble 40W 4ft T12 tube, there exists 3 official standards/versions
FD-40-E-G13-38/1200
60081-IEC-2440
which is a Switch-start/external starter tube
FD-40-L/P/H-G13-38/1200
60081-IEC-4440
which is a 8V High resistance Cathode tube
FD-40-L/P/L-G13-38/1200
60081-IEC-5440
which is a 3.6V low resistance cathode tube
the "FD-40" string is the ILCOS code for each type and the 60081 is the IEC data sheet number for each type for anyone else who wants to sleuthing
it is generally accepted that a switch-start tube will have High resistance cathodes, (if you look at "both cathodes in series" resistance value under the info for ballast design heading in the IEC 60081) but that is not always the case nor is cathode resistance/voltage actually controlled or defined for those tubes
cathode voltage and cathode resistance is only explicitly controlled/defined for the 8V and 3.6V tubes