WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
Building, troubleshooting and testing of these amplifiers should only be
performed by someone who is thoroughly familiar with
the safety precautions around high voltages.
I've built a few Aikido circuits and (if I understand you correctly) the "Aikido Cap" serves to feed the power supply noise into the bottom grid of the output section. I can't see the sense using the expensive stuff there. I use Solen or Sprague orange drops in that position. Maybe I'll get a chance to try the mundorfs for coupling caps - but I have only Jensen copper foil budget, max. Some vintage PIOs sound good to me as we'll. Not all, but some.
That is a difficult to answer question, I think. I really comes back to the larger question of the audibility of capacitors in A.C. coupling applications. Although, in the Aikido circuit, it is power supply noise that is being A.C. coupled, a component of that power supply noise will be due to modulation of the power supply by the music signal itself. So, I think it's conceivable that the capacitor quality may be audible. The only way to know for sure is to try installing a better cap. and listen for any improvement to the sound. That's what's both fun and frustrating about this hobby, ultimately, everything must be judged by listening.
Capacitor quality is almost irrelevant when it is handling a large audio signal. It will be completely irrelevant when all it is doing is handling a small correction signal.
I don't advise the OP to spend 'more' on any caps. Just make sure the coupling cap which sets the LF rolloff has an appropriate dielectric (e.g. perhaps not polyester), and is of normal good commercial quality.