I assumed that since the resistor would be between two out of phases sources the reduction by phase cancellation would average the frequency response to some degree. ...
That's a cross-line master volume. All it winds up doing is adding {Signal} to {-Signal} to reduce the net drive to the output tubes.
... would a large resister placed after the PI (where a cross line master volume or cut control would go) create the same positive sonic effects as standard negative feedback? Spikes in the frequency response and other aberrations would be cancelled ...
But how does the new cross-line negative feedback force any change of operation? In fact, how does feedback cause any change of operation the way it's normally used? [Questions to ask yourself]
Feedback reduces distortion at an amplifier's (single gain stage or entire amp) output by comparing the output signal of an active gain stage to the input signal; where there's a difference, the feedback loop takes some of that stage's gain and throws it away (which makes it
negative) in the process of counteracting the change/difference between input & output.
And the "change" which is counteracted is distortion.
Along the way, some other effects happen, such as raising or lower of internal or output impedance. Which change is made, and in what direction, depends on how the feedback is derived from and applied to the amplifier.
I assumed that ... the resistor ... would average the frequency response to some degree.
"Averaging frequency response" sounds a lot like "equalization" to me. That's a lot to ask of a humble resistor, who responds to all signal frequencies essentially the same.
And since this resistor is only on the output of the phase inverter, it doesn't compare output to input. Instead, it's only comparing 2 different outputs. It has no gain of its own to "use as muscle" and throw away in order to force a change.
This is probably a good time/place to talk about feedback & how it works. Or not... You were talking about "evening out spikes in frequency response." Since that sounds like EQ, it's probably good to ask whether we should focus on the goal (EQ) or the means of reaching the goal (possible NFB implementation).
Which one do you care about?