Welcome to "Synergy" 101(which we could get into impedance matching but we won't)... First off an integrated amp simply is an all in one device more or less, some even have tuners for that old thing called AM/FM radio...
However fact is that when you take a preamp section and Amp section all in one normally they share the same power supply, and same chassis which can sometimes make power and noise available go up and not be as balanced as separates.
This has nothing to do with you issue or question, bottom line is using an integrated amp for -JUst the amp section- Or Just the Preamp section separated if you have removable jumpers to do so, still does not totally eliminate the power draw on the internal transformer, you are still powering 2 devices of the audio chain even if you not using one of the halfs, its the same as a Receiver by the way, they just like to call integrateds "integrated" amps in high end audio, and if it has a Tuner on board as mentioned above its basically called a Receiver like you buy at your local best buy.
Only reason I could see anybody using another "Volume control" or Preamp outside of the internal integrated amps would be for adding a preamp with Phono stage etc... If the integrated did not have one, or a better one..... However again this will totally depend on the integrated amp and how good it is, or if its got a really good Amp section and crappy preamp.
Bottom line is I would NOT run another POWERED ACTIVE preamp into the CD input or something on an integrated amplifier and Set the Volume on the Integrated amp to 12' oclock and adjust the volume on the other device as this will simply add more GAIN more Noise... The other thing some might do this for is to try and get BASS and TREBLE controls off one unit because the other does not have it etc... But it gets silly to add more cables, more Power supplies and you should just get one unit that you are happy with or go Separates all together.
By the way the only way I would consider even plugging a preamp into an integrated is not by using the integrateds inputs hooked up to the preamps main outputs..
Integrateds that are correct for this use are ones like a Mcintosh that has a MAIN LINE IN AND MAIN LINE OUT, which has REmovable Jumper bars to Totally disconnect the internal amp and preamp section from each others signal entirely.. BUT recognize I stated disconnect the "SIGNAL" this still does not disconnect the preamp section from Drawing precious power from the Transformer supply.
May I ask why you want to do this? If you have old devices laying around and wish to just do it I understand, but if your buying something don't worry about all this stuff and do it right to buy what you need.
Actually let me correct and clarify 3 reasons I could see someone trying to add a device with separate volume to an integrated.. #1 a Phono section is needed,
# 2 The amp section is good on the integrated and the tone controls are needed on one device or the other
#3 somebody is trying to Cheat by getting a Remote control onto an old integrated amp by having an updated preamp outboard device with remote volume capability.
I wrote all this very fast, so hope its clear enough :-)