In the audiophile world and even in the musician's world, for that matter, there has also been some debate regarding the "sound" of one interconnect cable vs. another.
The reality is simply this: EVERY component, be it a power tube, a guitar cord, an RCA cable, or any other component in the audio chain has measurable characteristics: Resistance, capacitance, and inductance. The values may be very low, or very high, but they are never true zero nor truly infinite.
As such, these devices are an RLC filter. They WILL affect the system frequency response. By replacing one tube, or one cable, or one capacitor, with another type, even one with the same primary value (as in, a .022 uF capacitor replaced with a different type .022 uF capacitor, with a different type of construction, causing it to have slightly different R and L values), this will affect the frequency response of the system to some degree. If the change is large enough it will be audible. If it's small enough it will barely be measurable.
So, no, tubes (and cables) don't have a sound of their own but they do affect the system frequency response. This is why "different power tubes sound different." It's not the tube, but it is the interaction of the tube's specific parameters within the total circuit, affecting frequency response.
So...let's not split hairs. For a specific tube amp, swapping out tubes can alter the tone depending on the characteristics of the tubes being swapped.
But....two cables, having identical electrical characteristics, identical RLC values, and being of two radically different construction types and price points, will have an identical "sound" and so would two tubes that have identical electrical characteristics, but are physically different in design and construction. It is possible for different tubes, or different cables, to result in the same sonic result. If their parameters are the same.