Yes, but physics does not tell you that a fuse can't affect the sound quality of high-end equipment.
Not the fuse, but Voltage drop across the fuseholder. You can measure it just like you can Voltage drop across a power cord.
Some equipment does
not care (for example our MP-1 preamp, whose power supplies are heavily regulated) and
some equipment,
especially that which has a heavier power draw and no feedback, like our MA-1 amplifier, does.
SETs will be prone to 'sound differences' of fuses and power cords since they have no feedback. Our class D amplifier, which employs about 37dB of feedback and has low power draw at idle, is pretty well immune to fuse and power cord changes. Feedback in high enough quantity (and properly applied) allows the circuit to reject that which is not the signal.
I recommend to our customers to avoid boutique fuses as they are expensive, don't always blow at their rating (may be higher or lower) and because the Voltage drop across the fuseholder is
really what you are hearing. In most fuseholders the fit is not perfect. So sometimes you get lower Voltage drop by reversing the fuse, which has led to the myth that fuses are directional. You can get the same effect by simply spinning the fuse slightly to obtain a better contact in the fuseholder. A measurement of the Voltage drop will confirm the correct positioning of the fuse in the holder.
I think a lot of tube life also comes down to how hard do you run them...My Mercury rectifier gets run hot. As such, I seem to fry them about every 1000 hours.
FWIW a mercury rectifier has poor application in a modern tube amplifier. You're better off with HEXFRED devices, which are super fast and super soft recovery and can handle currents far higher than most tube amps might draw and can be made to be lower noise quite easily.
Mercury vapor tubes are used to reduce the Voltage drop across the rectifier and are also high current, usually much higher than you see in conventional rectifiers like the 5AR4. For this reason they were used as rectifiers for charging batteries and the like. They are also
very reliable (and so can last decades) since the mercury cathode is self renewing. If yours are failing the application is
really not right or may indicate that some other component is drawing far to much current. I'd get that sorted out if I were you!!