Yes, that is correct, but if you are starting with a cathode taken from a new gun intended for a modern tube, then the cathode should still be unactivated, as the gun was never sealed into a tube. The activation of the cathode takes place while the tube is being pumped down, so that the liberated gases can be removed from the tube. The getter is fired once the tube is sealed off from the pump.
It seems highly unlikely that a modern cathode assembly would mechanically fit the older guns, though. The cathode/grid spacing is highly critical for proper cutoff, with tolerances measured in thousandths of an inch.
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