Forgive me if I missed something, but maybe one of the big benefits of the TC is that you are able to AF better on small birds at a distance?
I have had some moments where the R7 with the RF 100-400mm was not able to detect the bird because it was too small in the frame. I was considering the TC for these instances.
Jeroen
Clearly the RF 600mm F11 gives more reach the the RF 100-400mm with 1.4x TC effective 560mm F11. IMO, IQ is much better with the 600mm as well as well as AF as well. Add to the fact that the 1.4x TC is not that much cheaper than the 600mm F11, it's a no brainer for me. I use both the 600mm and 100-400mm depending on the distance the subject(s) are away. If too far away, I simply don't shoot. Cropping too much rarely seems to give great results for me.
Thank you for your answers Bigger and Steve! Very interesting considerations.
Also thank you Alistair for pointing out not everything translates from theory to actually using it. I fully agree with you, but I have to say I have respect for people who take the time to test setups and combos to help answering the question from OP.
I would like to add that I agree the IQ will not improve in any way with a TC. But even without a TC the IQ would be poor when shooting at a fair distance. For me personally I only take those photo's to identify birds when I can't identify them in the field.
Jeroen
Well, as I said, theory is one thing, but often practice is very different. What I want to know is whether using a 1.4X converter with the RF100-1400 on my R7 will be beneficial for me, given what I shoot, how I shoot it, and how I process and display the results. So I just did a quick comparison test, shooting a tree at a distance that represents the close end of the range I actually use that lens (with or without extender) for. I then processed the pictures the way I process all my pictures (I have a preset I use with DXO Photolab). And then I cropped both images a reasonable amount, which is what I do with most of the shots I take with that lens. I cropped both to give the same field of view, which meant cropping the 400mm shot more than the 560mm shot, of course. I then exported both images as JPEGs downsized to 2000 pixels on the long side, which is how I display most of my images. Viewing those JPEGs on a modern monitor is roughly equivalent to looking at a print that's anywhere from 10 inches across to 20 inches across, depending on your screen resolution. What I discovered is that yes, you do get a benefit from using the extender. Here are the downsized images, first the whole frame:

Focus is on the dark knot at the center
And here are the two crops, framed as close to each other as I could without spending even longer on this than I have already:
To my eye, the 560mm shot has a bit more detail. It's not a huge difference, but it's enough to make it worth using the extender, especially because you do get the AF advantage with having a closer in field of view.
When making decisions about this, there's really no substitute for actual experience, and experience that's relevant to what you're going to be using the lens for. Talk of airy disks and extinction resolution is all very well, but it's often not just confusing, but actually misleading. For all I know, the lens + extender combination wouldn't be advantageous for other processing plus display choices, but the only way to know is to actually try it.