Does not using an interpolator mean that my GPSDO is useless, or does it only mean that it takes longer until it locks? I mean - after 1000 sec, I can also measure 1 mHz frequency deviation. I expect the ideal loop time constant being around 1000 sec.
Using a time interpolator for getting the "numeric value" of the phase difference is required when you want to get the precise information at each sample interval (ie. you get 10000000.5673 counts as the result at each sample).
When not using the phase value your measurement is of +/- 1 count resolution and you have to average those "integer" counts within say 1000secs to get the "fraction of the 1 count" hidden inside (your "milliHertz resolution").
Both methods are theoretically "identical" when talking longer measurement periods (and some other assumptions).
..but next time with an analog interpolator :-) can you give some hints about this topic?
All modern ($$) counters use a kind of an interpolator.
The analog ones are easier to make - ie. a ramp generator started by ref edge and stopped by the signal edge and the actual ramp voltage sampled by an 10-16bit ADC (for example 0.000ns phase difference reads 1Volt and 99.999ns reads 4Volts off the ramp, provided your 1 count is 100ns). The ramp generator could be a simple capacitor charged via a current source (to get a linear readings).
The ADC value is then converted to the "1 count fraction", and combined with the integer counter's value (or better to say "combined with the counter's ratio") you will get those 10000000.5673, as an example.
What the modern counters also do is they use "sampling" of a continually running counters (ref/signal) without zeroing their values between the measurements (and they do "new-old"). Therefore you are not loosing the phase's trend information.
That counters are ie. called "reciprocal counters with time interpolators". You may do, for example, 1000 measurements/samples per second with a milliHertz resolution (with some math involved).