It is accurate to say that any teleconverter reduces image quality to SOME extent. It really depends upon the lens/TC combo though. Some work very well together, so that there's no significant loss. Others, not so much.
Generally speaking, prime lenses work better with TCs than zooms do. This isn't a hard and fast rule. Just a generality. You need to find someone using the exact same lens with the exact same teleconverter... or just buy and try, from a place that allows returns in case the results aren't up to your expectations. I can't tell you how well the Tamron 100-400mm works with teleconverters. I can tell you that the Canon EF 100-400mm IS USM "II" works extremely well with a Canon EF 1.4X II. That's a combo I sometimes use together. (I also use that 1.4X II on EF 135mm f/2L, 300mm f/4L IS, 300mm f/2.8L IS and 500mm f/4L IS lenses. I've also got Canon EF 2X II that I occasionally use on EF 300mm f/2.8L IS and more rarely on 500mm f/4L IS lenses, but not on any zooms.)
1.4X teleconverters generally have a lot less impact on image quality than stronger 2X teleconverters.
One thing you need to watch out for is that the Canon teleconverters have a protruding front element. That needs to fit inside the rear barrel of any lens they are used upon. Many lenses don't have large enough rear barrel OR have rear elements that might interfere with the teleconverter. The current Tamron and Sigma APO 1.4X teleconverters also appear to have slightly protruding front elements, although there's less protrusion than the Canon.
If it will fit, you might consider the Canon 1.4X II... the older version... used. It can be found for considerably less than the current III sells for new. The optical quality of them is very similar. I'd challenge anyone to tell apart images made with these two versions of Canon 1.4X. I just found a used 1.4X II at B&H Photo in top condition for $219. That's half the price of the 1.4X III new.
The earlier Kenko 1.4X TCs I've had some good experience with. They are much more affordable, yet are pretty good... and they don't use a protruding front element, so can be fitted to a wider variety of lenses. I have had no experience with the current "HD" Kenko, which prime claim to fame is that they can accommodate both EF and EF-S lenses. (They're the first TCs that can do so, I think... though IMO there aren't any EF-S lenses that it would make sense to use with a TC... maybe the EF-S 55-250mm, though I would expect a pretty strong hit to IQ and pokey autofocus.)
If you can find the previous version Kenko Teleplus 1.4X "Pro 300" DG (or DGX), those are quite good and affordable.... sold for around $160 new. The "Pro 300" version has good image quality from corner to corner, so might be a better choice for a full frame camera such as you're using.
On most lenses, the even less expensive Kenko Teleplus 1.4X "MC-4" DG (or DGX) is actually one of the sharpest TCs I've seen...
at the center of the image. In fact, it rivals the IQ of the Canon TC's, but the Kenko MC-4 goes a little "soft" out toward the corners of the image area. This wouldn't be very noticeable on an APS-C crop-sensor camera, but may be on full frame. Of course, in many cases some corner softness also doesn't matter. It might even be desirable in many images. I don't know current pricing, but the Kenko 1.4X MC-4 originally sold for around $125.
The Kenko teleconverters' "DG" and "DGX" designations represent some slight changes in the electronics. The DGX is a later version that might offer some slight improvement in autofocus performance... but not enough to worry about, IMO. With a 1.4X teleconverter on a lens that's already f/6.3 (so becomes an f/9 combo), I wouldn't expect great AF performance anyway. It's probably going to need good light. I don't have the Tamron 100-400mm and don't currently have any of the Kenko TCs... so can't really say how specific combos might work together.. But, for the money it might be worth trying one or the other of the Kenko.
Here are links for info about the Kenko 1.4X Pro 300 and MC4... The Pro 300 is still available new, but the MC4 isn't (if you want one, you'll probably have to track one down used)....
Kenko Teleplus 1.4X MC4 DGX:
https://www.bhphotovideo.com/c/product/674589-REG/Kenko_MC4AF1_4DGXC_TelePlus_MC4_AF_1_4X.htmlKenko Teleplus 1.4X Pro 300 DGX:
https://www.bhphotovideo.com/c/product/674565-REG/Kenko_PRO3001_4XDGXC_Teleplus_PRO_300_DG.htmlThis is the Canon 1.4X II that I use now:
https://www.bhphotovideo.com/c/product/801956188-USE/canon_6845a004_1_4x_ef_extender_ii.html