No. At least not on a stock iPad.
Apps can not 'usually' affect each other. Jailbreaking can get around this for some things, but I don't know if there is an app for this thing. The people in the Hacking area probably know.
There is an app named Audiobus that can connect different audio apps together, output to input, but it only works with apps that specifically add support for it. That would include Apple's app Garage Band, from which you can conclude it's mostly about music creation tools.