Muddying the waters with the original question:
How important is the tube rectifier sag to achieving that great vintage clean sound/feel?
It depends on what the player considers "vintage" sound/feel. Some vintage amps had sag, some didn't.
It depends on how you define sag and whether that's slang for voltage droop due to poor regulation, or if it's a sonic effect. Voltage droop when pushing max power might lead to the sonic effect of compression. Yet a Champ, which should have a largely constant supply voltage because current draw is nearly constant also has compression when it's heavily distorted.
Onset of output tube distortion (and preamp distortion in the case of master volume amps) will probably give some impression of sag/compression.
Is sag evident at low volume when you're not really pushing the amp, just because the tube rec. is there?
No, it isn't (or
shouldn't be).
Here's why:
Assume you have a class AB amp. You already know that what makes it AB is that after some amount of drive signal, the tube(s) on one side of the OT will shut off while the tubes on the opposite side conduct much more current. However below that drive point, one side draws less current as the other side draws more current. When both sides are conducting, the action of one side is then offsetting the action of the other, and current drawn from the power supply is largely constant.
If current draw is constant, or varies only slightly, the voltage dropped across the rectifier or power supply impedance must also stay largely constant. So "sag" caused by voltage drop can't occur, can it?
It's my opinion you can't really evaluate sag/compression without pushing the amp close to its output power limit. However, you
can evaluate the amp's tone at any volume setting. If you like the tone/response at low volume, then you like the amp. It may respond differently when pushed, or not... you have to crank it up to find out.
I never played on stage much; I loved the sound of all my old Fender amps even clean at low volume. All seemed to have a warm, tubey response that was nothing like the solid-state amp I had when first picking up the guitar. Apparently, sag wouldn't be the (only) deciding factor in my case, for my taste. But no one has to agree that what I like works for them, so you really have to try for yourself to find what works for you.
... I played a Deluxe Reverb re-issue ...
Would it be silly/stupid to build this amp type and not use tube rec? ...
I never measured current draw of the Deluxe Reverb during driven conditions. I have a hunch that with 6V6's, the amp doesn't draw
massive current from the power supply, so with a GZ34 (lowest voltage drop in a common guitar amp rectifier) the sag is probably minimal. That said, filter cap sizes enter into the equation. But the fact that players can generally perform with a band in a smaller club with a Deluxe Reverb tells me it has a certain amount of punch.
If you're building from scratch, why couldn't you have both a solid-state and tube rectifier, perhaps with a switch to select which you're using. You could compare for yourself and see what you like. Note that the lower voltage drop of the solid-state under all conditions will mean some amount of tonal difference just due to higher supply voltage throughout.