Ray,
The Hammond (or any other electronic) organ is definitely an electronic instrument, whether it has an amp on board (like a Hammond) or has to be used in conjunction with an external unit (eg, like a Vox Continental).
It is true that the Rhodes piano (just about) makes a sound unamplified (the same was true for certain other electric pianos of the period, made by Hohner, Selmer, etc), but except that it needs a power supply of its own, it is entirely analogous to a solid guitar: it is not a complete instrument in itself. You could only describe it as a complete instrument if it had built-in amplification (and if I recall correctly, perhaps some models did).
I have never heard anyone refer to an "electric microphone". With one exception, though, microphones are another part of a (whole) electronic system since they are of no use without some sort of reproduction equipment at the other end of the cable, whether by way of amplification, recording or broadcasting. The exception is the original telephone system wherein a carbon microphone (in effect, a variable resistor with a value dependant upon received soundwave pressure) simply modulated an applied current so as to create a signal which could heard in a dynamic earpiece. No hint of thermionic valves or solid state semiconductors (until later).
In short, if what we hear depends on valves or solid-state devices, or both, it's an electronic instrument.
I'm sure I read all this when I was about 12 or 13 and newly interested in the electronic side of music and sound; I didn't make it up for myself (though I believe I am capable of having done so).
