Not with a headphone amp (yet) but I've seen a number of tube radios degrade over time.
Heat destroys components, so the longer something is on, the more likely the capacitors, filters and resistors drift out of spec and stay there. Usually, that muddies up the sound a little and makes them drift in station lock, as well. Amps are less complicated, but you can still hear problems in amplification sections once you've fixed the rest of the circuit.
Sometimes, it's fun to turn the set on (safely) between replacing each component. You can literally hear it shape up and start sounding good again, bit by bit.
To answer your question, yes, even the modern components will drift and change value depending on heat and age. Eventually, they fail. I haven't listened to a poly cap or a film resistor fail yet, but you can hear it in the wax/paper caps and carbon resistors.