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A 8086 processor requires approximately a maximum power of 1.8 watts, it means if you want to power the CPU from the power of the clock, the clock signal generator needs to be a radio transmitter with an output power of 32.5 dBm, not including insertion loss and power conversion loss at the load. This is beyond the maximum transmitting power of Wi-Fi allowed by the FCC. And it's a square wave clock, a 1 MHz clock can contain frequency components up to 100 MHz (or 1 GHz in modern digital logic), blasting out RF garbage everywhere. Just imagine the electromagnetic interference.

A typical crystal oscillator has a drive level of less than one miliwatt, 3 orders of magnitude lower.

But in principle, yes, I don't see why it's impossible.