Of course it has relevance.
If the input1 doesn't have the secret sauce, and thus has a higher noise floor, then the entire system noise-floor level is necessarily higher, because that noise at the input is amplified by your real amplifiers front end, looped back around through the effects loop back into the FM3 into another input that won't have secret sauce, and then back into the amps return. You've got two points of digitization there that can be sources of noise. Any noise upstream from the amplifier is going to make the system noisier.
Semi-related, but I did a bunch of measurements on noise in 2022, and this is how a bunch of my stuff came out:
View attachment 146861
These aren't 4-cable-method measurements. So any of this gear in a 4-cable-method setup - or more traditional effects out front and in the loop type setup - are going to be noisier. To what degree, it is hard to say. But clearly, noise floor is something that raises (sometimes very significantly) when you introduce AD/DA conversion.
Recently I compared the Quad Cortex, Helix, and Axe3 in front of an amp too. And that is exactly the ranking - Quad Cortex is the loudest, and definitely requires some kind of noise gate when hitting the front of a high-gain channel, Helix is the middle child, and Axe3 is the quietest; for my amp I have to use the boost/pad feature at 18dB.
Now I've never heard the FM3, so I can't comment too much. All I can say is, I've seen a lot of reports about it being noisy and finnicky to setup in 4-cable-method. I believe Cliff has even said that it isn't truly designed for that purpose, and that people are better off using the FM9 or Axe3... or now... VP4.
I could be wrong on that last point, but it is my recollection at the moment.