Is it a regen?

 The question is can you build a regen around an opamp?

 Things to consider:

How do we modulate and demodulate an AM signal.

What is the number one requirement for mod / demod?

I produced some screen shot that help answer the question.

I have some wheres to be shortly so am just posting the screen shots now 

and will comment further later. 

The shots are in reverse order. Reading from the bottom up makes more since. 

Using one input create an audio output.

Adding a filter separates the signals.

Driving with an AM signal you can see the distortion created. 

Here I tie the inputs together and we see distortion (ripple). This is the non linear action required to demodulate.

 The plus and minus inputs are inverting and non-inverting. Here we have the same phase out as in. The shot above inverts.