In some element controller custom chips I've done,
Vg was supplied and sensed (for sequencing; if not
proper, do not apply drain power). In discussions with
the MMIC designers that my chip was to support, it
was said that the Vg (gate) voltage needed to be very
low noise - ripple there will modulate the carrier making
some nasty spurs. My chips included "active bias" amps
to drive Vg such that drain current sensed, was on
target. Applying a fixed Vg is only good if you have
fixed conditions (temp, supply, MMIC processing
variation).
So I would suggest to you that a simple charge pump
is probably going to get you as far as functionality,
but pollute your output spectrally. You'd need a good
linear regulator with decent high frequency PSRR to
clean up any switching converter produced supply.
And having this on chip is almost certain to put all
kinds of nasty onto the local ground, which can kill
you the same way.
Maybe you don't want a peanut butter and hand
grenade sandwich, is all I'm saying.