We compare these two schematics. The TPA3116 is used as signal generator.

We set the volume to a fixed level. Then we measure the current over the high-side resistor by measuring the voltage drop over a smaller (22Ω) resistor.

test name	description
A	No parallel resistor, 440Ω load
B	22Ω resistor, 440Ω load
C	No parallel resistor, 2kΩ load
D	22Ω resistor, 2kΩ load

freq	mA (A)	mA (B)	mA (C)	mA (D)
200	46.4	41.8	26.6	21.5
300	46.4	42.7	27.3	21.5
400	46.4	41.8	27.3	22.2
500	44.5	42.7	26.5	22.9
600	45.5	43.6	28.4	23.0
700	45.5	41.8	28.4	22.9
800	46.4	41.8	28.7	24.8
900	48.2	43.6	28.7	22.9
1000	48.2	43.6	28.7	24.7
1500	48.2	41.8	28.0	24.7
2000	48.2	44.5	29.5	25.1
2500	48.2	44.5	29.8	25.8
3000	46.4	41.8	28.4	25.8
3500	46.4	43.6	28.4	24.0
4000	46.4	41.8	28.4	24.0
4500	46.4	41.8	29.1	23.3
5000	47.3	43.6	28.7	24.4

We are looking for a flat response, all tested setups deliver. What we can conclude here is that the parallel resistor doesn't do anything for this specific test.

We set the volume to some nice level, then we replace the 440Ω resistor with a different load, we measure the change in current.

Then we attach the parallel resistor, turn the volume knob once more to a nice level, and repeat the process.

Resistance	Current (No parallel resistor)	Current (Parallel resistor)
220	26.4 mA (+15%)	26.7 mA (+18%)
440 (baseline)	22.9 mA	22.5 mA
660	20.3 mA (-11%)	20.0 mA (-11%)

That wasn't very conclusive, perhaps we have to up the resistance?

Resistance	Current (No parallel resistor)	Current (parallel resistor)
0	47.2 mA (+159%)	50.5 mA (+177%)
1000	27.1 mA (+49%)	27.3 mA (+50%)
2000 (baseline)	18.2 mA	18.2 mA
3000	13.8 mA (-24%)	13.8 mA (-24%)

Conclusion: the parallel resistor doesn't do anything until we get to really low resistances, then the parallel resistor makes it worse.

For the tested amplifier/transformer combo, the parallel resistor does nothing useful.