Will I benefit from a subwoofer with 20Hz speakers?

Eric, I do not wish to prove you wrong.  In fact, since I know your existence in the forum and read several post of yours, I always respect and consequently place more weight on what you have advised or recommended to improve my system.  So far, except last time you said to toe-in speakers and cross in front of you that I found by doing so shrinks the width of soundstage, everything else is spot on.  Unfortunately, this is another incidence that I was (and I believe some others were) not convinced.  Let me explain by telling you my experiment first.

I use foobar2000 as a player and under the "View" "DSP" you should be able to find "Equalizer."  The reason I specifically refer to this particular EQ tool in foobar2000 is because I found this is probably the best EQ among all the players I have experience with.  I trust the fidelity of this tool.  The lowest frequency this EQ can go is 55Hz and you could adjust all bandwidth up and down by 20dB.  I play a track entitled Keep A Secret by The Whitest Boy Alive from their album Rules which begins with heavy weighty drum beats.  Then I gradually ramp up the 50Hz-156Hz bandwidths in a linear fashion, i.e., starts with +1dB at 156Hz, +2dB at 110Hz, +3dB at 77Hz and +4dB at 55Hz and ramp up by a certain level while keeping the slope linear.  When ramping up the 55Hz to roughly halfway (+10dB), I have already hear distorted bass notes.  I stopped with the worry ruinning my speakers.

The reason I did this experiment is because I suspect that what you and the other forumer have measured in your room as shown in SPL down to 20Hz might be some highly distorted noise, not the pleasant musical notes any more.  That is also why I am asking you to provide some quality recording to the group demonstrating what we are going to hear when you tune the speakers from the rated frequency (say +40Hz) down to 20Hz.  I could be wrong and I wish I am wrong.  I wish the tuning / DSP is successful out of the room treatment so we could all enjoy/benefit from this experiment.  I hope I make my point this time. 

I will play the devils advocate here. While adding a sub has the potential to add LF quantity and / or quality, it will invariably take away from the signal strength going to your main amp / speakers. That is, you need to make compromises at the low signal level, which might be quite steep especially when the subs plate amp with super low input impedance guzzles the current away from a tube power amplifier with high input impedance.

In easier to understand language: most of the energy that drives your system will be shunted to drive the subs, and your amp driving the main speakers will be starved and get only the meager leftovers that the sub graciously allows.

I have invariably found that adding a sub always has noticeably degraded midrange and high frequency quality in my systems, and the gains at the added bass level were not big enough to balance out the losses in the main frequency range.

I use very high efficiency speakers and straight path / no feedback system approach. However, when you have a preamp that has an added stage (or stages) to provide current drive for the sub(s) then this is a non-issue. 

Yet, the problem of those extra stage(s) eroding low level signals still remain, so the main amp will receive compromised signals regardless a sub is connected or not. No free lunch, but we can plan when we understand the menu.

"...most of the energy that drives your system will be shunted to drive the subs, and your amp driving the main speakers will be starved and get only the meager leftovers that the sub graciously allows."

That should not the case if the sub is active.  The main speakers will not be affected much but if you have high-pass filter (HPF) in between, then it will leave more headroom for the amplifier to dirve only the mid and high and therefore more efficiently.  In fact, I found, without HPF, the integration of sub with the main speakers wont be as good because the mid-bass was often boosted a bit hig to my taste.

I will play the devils advocate here. While adding a sub has the potential to add LF quantity and / or quality, it will invariably take away from the signal strength going to your main amp / speakers. That is, you need to make compromises at the low signal level, which might be quite steep especially when the subs plate amp with super low input impedance guzzles the current away from a tube power amplifier with high input impedance.

No, this isn't a thing.  With preamps easily able to under 1 kOhm loads, and amps  presenting 25k Ohms and higher loads there is a barely measureable change to the preamp output at the same setting.  Do the math.  Assume a perfect voltage source with a 1 kHz output impedance.  Takes a lot of 25kOhm amps to cause a change.

@dmilev73  Yes you will definitely benefit from a sub or 2 or 3  When this is suggested people think of being overpowered by thunderous bass which if properly implemented is not that at all. Think of the subs as tuning devices. An enlightened poster mentioned a SWARM and I encourage you to read up on this. (aka DBA)

But the thing is that rooms and speakers are random.

This comment displays a lack of understanding. If nodes developed randomly it would be impossible to treat them because you have a moving target. Any given speaker in room will set up a consistent pattern if nothing is added or removed and the doors, windows and drapes are left as they were when first measured. Come back in a week or a month and the room will measure exactly the same.  Nothing random about it.

@lanx0003, Who told you to toe-in your speakers to cross in front of you? This relies on the proximity method and works with speakers that use constant directivity waveguides and a power response that is even.  A 180 degree waveguide, like the ubiquitous dome tweeter will not work which is probably what you have. A CD waveguide toed-in like you tried provides great imaging and a nice w-i-d-e  listening area.