Everything makes a difference. Whether it is a difference that you can hear is a different question. Whether it is a difference you might consider an improvement is probably the most important question.
Back when I got my C-melody sax, the original pads were long gone and it had what I found out later were Conn reso-pads. These were just tan leather pads with a stiffer card behind the felt, not resonator pads like we think of today. I had to replace a few so I ordered the same kind to be consistent. It plays and sounds OK, but in the lower register the lowest notes always seem too loud and unbalanced to my ear. That's also where the pads are the largest diameters and would have the biggest influence on tone and projection.
Later I picked up a Frank Holton C-mel that someone had attempted to re-pad with a stock pad set most of which didn't fit the cup diameters and all of which were far too thick. The method to attempt getting a good seal was to bend the pad cups down onto the tone holes, and of course that didn't work at all. The whole upper stack was a mess that was impossible to get anything to seal or regulate. A good number of the original pads were still present on the lower stack (project horn abandonment on ebay time) and these were very soft pads, thin, white leather and felt only and had that stitched dimple in the middle. Most of them still sealed. It made me wonder what original functionality in the upper stack had been wasted.
There are many young players who get these old C-mels and deck them out with the metal resonators, and then you hear nothing except how unbalanced they are and how the intonation is compromised, etc., etc., and inevitably they blame it on the early saxophone design deficiencies.
This is like equipping an English racing bike with oversized tires and complaining because they pop off the wheels when inflated.
I checked with Prestini and they are willing to make a set of original type pads for the Frank Holton, so I can see how it was supposed to originally perform. It's been all torn down for months and whoever tried to force fit the wrong pad sizes mangled just about every pad cup on the instrument. When I really get bored I pick out one to work on for a few hours. One by one these are getting close to being able to install. I'll probably take Prestini up on the soft pad custom run. The cost would be about the same as resonators and I can see how one of these C-mels sounded originally. I think these were intended to have a more mellow tone and play at a lower volume than a big band saxophone.
It's all fine to experiment, and I understand your investment in the instrument was low, probably the same situation with whoever attempted to re-pad the Holton. There is a tendency for us to think of an instrument that didn't cost us much as an opportunity to experiment. Perhaps. On the other hand we might look at it as if we got a great deal on a restoration opportunity rather than a hot-rod candidate.