Is there a way to record 'on board' audio on iPad? Related to this question: What cable do I need to go iPad audio out to macbook air mic in? which is asking about cables to record iPad audio on another device. 

This question is: is there a way to record audio generated on the iPad on the iPad itself? For example, are there any audio recording apps that can record in the background while audio is being created in another app? 

It's a bit hard to search for as there are a lot of apps that allow you to record audio via the external mic, but I'm specifically looking to record audio generated from the iPad itself (such as from a synthesizer or drum machine app).
In general, no.  On a stock iOS device, the OS security sandbox prevents any app from recording, or otherwise accessing in any way, the audio generated by any other app, unless that other app explicitly exports its audio (via AudioBus or Inter-App Audio).  Some (but not all) synthesizer and drum machines (etc.) apps document support for such.