Yes, the principle would work. It's the standard instrumentation amp with variable gain configuration. The AC and DC paths are separate, so set the original source resistors for the minimum gain required when paralleled with half the pot. Put a resistor in series with the pot to set the maximum gain.
You would have to adjust the grid bias voltage to cope with the changed source resistor values and still leave working headroom.
You're left with two problems:
(1) What to do with 2 (or more) FETs in parallel.
(2) What do do about d.c. imbalance between the + and - FET paths.
Take (2) first: since the circuit is AC coupled anyway, you can use a large non-polarised capacitor in series with the pot.
So for (1), and this is a bit iffy: split the "max" resistor referred to above into two equal values. Use 4 resistors of this split value, one from each FET source with a blocking capacitor to the relevant end of the pot. In this way, the FET sources are not directly shorted together.