I am speaking of a low-volume playing situation, but it shouldn't require high volumes for such things to be audible.
So nah. Nothing like that. It's a question both of how the pedal treats the bandwidth of the signal throughout the circuit, and also a question of the guitar itself. One of the things I dislike about guitars like an SG with a pair of P90s is that the pickups are so close together, and have so little high end, that there is precious little tonal contrast between the neck and bridge.
And its not a question of a pedal delivering different tones for different guitars, but whether switching between neck and bridge with the pedal ON yields as much of a tonal change as switching pickups with the pedal OFF. And if doing the latter doesn't yield much change unless you pick a certain way, then one should not expect a pedal to change that. So, the pedal may indeed sound different with a Tele than with a 335, but switching from bridge to neck on either of those guitars may yield very negligible difference. Like I say, some fuzzes are like that. Doesn't mean they are bad pedals. They just don't have the trait of responding differently to different input.
And, similarly, there are fuzzes/distortions where rolling off some of the highs with my bidirectional tone control interacts with the input of the fuzz to produce near cocked-wah type resonances, and others where I can rotate the tone any which way I want, and I'll be darned if I can hear any difference. Just remember, we're talking about fuzz and not overdrives. Overdrives are more responsive to tone-control settings.
Same thing with distortions and wahs. There are some where sticking a wah ahead of the distortion delivers magic, and others where you can wah as much as you want, and the audible output from the distortion is only marginally different and not especially expressive.