Well....yes and no. Volume wise, you are taking a very small volume and making it only slightly bigger. But since the volume of the intermediate air passages of the average first stage, including the second stage hose, the inflator hose and the hose for the octo are still fairly small, doubling or tripling the lenght of the primary hose still adds a significant percentage to the total volume.
The difference in volume can be roughly measured just by turing off your air and seeing how many full and partial breathes breaths you get with the short hose and then the long hose attached. It can be measured much more accurately in terms of IP drop and recovery with the needle swing on an IP gauge during and after inhalation.
The difference will be there, but the difference also will not amount to a noticeable increase in performamnce.
It is kind of interesting that I have been getting reports from many Phoenix RAM owners that their PRAM breathes better than even a well tuned comparable RAM.
I tend to think that the difference is probably more related to the fact that most PRAM are equipped with silicone diaphragms, the best mouthpiece valves available, and are highly tuned (and perhaps also some wishful thinking or optimism). But, I have always wondered how much of a difference all the extra volume from the LP hose attachments could be making on the regulator performance.
I am referring to a double hose regulator were the first stage is the same as a Conshelf and the second stage is right next to it in the same brass body, no LP hose needed.
Comparing a bare RAM (with no LP hoses attached at all) to a PRAM with an octopus, LP inflator, etc. the ratio of volume from one to the other is huge.
I have tried testing one against the other, but the moment I add an IP gauge I am affecting my measurements since I dont have a real short LP hose. Any LP hose and even the gauge itself will affect the measurement (a classical dilemma in instrumentation design: any time you measure something you affect the measurement, to some degree).
The bottom line is that my observations seem to show that the IP does stay a bit more constant with multiple LP hose, but it is really hard to tell. In either case the IP variation is small enough that I would need better instrumentation (with recording capabilities) and a more controlled breathing simulator to truly be able to measure the difference (in the transient conditions of the breathing cycle). Again, I am not even able to test a truly bare RAM.