My inquiry is: Is it possible for this circuit to actually produce FM modulation?
Not one little bit. It would need wholesale changes.
V1 connects indirectly to V2 via a 2k2 resistor and this has zero effect on anything because V2 will remain exactly as it is and, inevitably, V1 becomes just a wasted and pointless signal that does nothing and achieves nothing.
V1 is the 1kHz AC audio voltage source.
No, not at all; you might just as well remove V1 and you will get the same result (with or without the varactor). Incidentally, the presence of the varactor (basically a diode) is just to rectify the output signal with some considerable losses.
I observed that when D1 is removed, the circuit behaves like an AM modulator with elevated voltage levels.
No, that's not what is happening at all; you are driving a perfect tuned circuit with a frequency that isn't quite at resonance and, this is what you will get.
D1, a varactor diode, is essential for achieving frequency modulation.
No, D1 will not bring anything to the party at all; it half wave rectifies the output waveform and limits the resonance of L1 and C1. You can see this when the diode is removed i.e. look at the much bigger and AC symmetrical AC voltage resonance (about 170 volts p-p). With D1 present you just get half wave rectification of the signal and killing of the resonance. Even if you used back-to-back varactors to avoid the rectification issue you still won't get modulation because your modulation signal (V1) does nothing.
I am looking forward to receiving a straightforward and easily understandable response.
Your circuit is fundamentally flawed (that should be easy to understand).
