Although I haven't been into Amiga for very long, I feel that what makes an Amiga an Amiga is the OS, the software, and to an extent, the custom chips.
I am of the opinion that it doesn't matter if custom chips are real or emulated, as long as they are present in some (perhaps virtual) form.
The OS needs a few features for me to consider it "Amiga", such as screen dragging and the ability to run 68k software. If something can run apps for the classic Amigas seamlessly, I am willing to call that thing an Amiga. If one can code 68k programs that bang the hardware on it and run them successfully, that, to me, is Amiga.
I don't care if it is PowerPC, x86, ARM, or anything else. If it can run classic Amiga apps and pretend to be 68k, that works for me.
However, an emulator running in an operating system doesn't really seem like Amiga to me. It needs to be seamless. Amithlon was a good example of this, I would consider it Amiga.
But then again, I'm new to the Amiga, so I don't really know that much.