I/O loops 3 and 4 on the Axe-Fx III support high-impedance sources. Also, they are unity gain.
So impedance and level are no obstacles. I tested this with some of my pedals.
Anything with active circuitry will still work with a high or low impedance source, but, your still losing the variable resistance and capacitance the passive pickups and tone/volume circuit introduces. When your change the input Z on the front input of the Axe, it makes a tonal difference, but its still not producing the same cleanup with a fuzz model. There are plenty of products that have come out over the years that are designed to chance the impedance after buffers or wireless, usually with inductors, though I've seen some plans that actually put a spare single coil pickup into the circuit, and have tone and volume pots even. That gets pretty good results actually, but, the form factor isn't exactly ideal as instead of rolling the volume pot back slightly while your playing you'd have to bend down and turn a knob.
Trying to combine what is still 1960's semi-conductor technology, and passive pickups, with modern active electronics is still an obstacle IMO. Things can indeed "work", but will the work the same ? NO. Are they close enough for some applications ? Sure, and there are a lot of circuits which have input buffers, pickup simulation transformers etc, built into them. Take the EQD Eruptor for example... cool pedal, but that transformer in the pedal sure doesn't like being around any power sources lol. Still though, not going to work the same.
Brian May runs his Treble Booster between his guitar and his wireless unit because it just won't sound the same otherwise. Guys build Fuzz Factory's into the guitar because if its behind a buffer or wireless you no longer can control the oscillations with the guitar tone and volume pots like you can when they are a physically connected part of the circuit. Etc etc.
If someone is happy with how a pedal sounds in a loop, or after a wireless, more power to them. Different isn't always worse, but different is different. If a big part of your tone you know and love is goosing your fuzz face with the volume pot backed off just a touch from 10, to like 9.5, and that sweet edge of breakup tone and feel it produces, your only going to be able to get that interaction with the pedal connected to your guitar.
I wish it wasn't the case, I've tried all kinds of load boxes, JRC reamp boxes, pickup simulators, you name it, because I really would love to be able to run everything in loops, and do things like run the Axe wah before a hardware fuzz pedal, but after a lot of time and money I've never had true success. Only true "solution" is running certain pedals into the front input, if you want them to behave in a specific way
Luckily, since most fuzz boxes with these "issues" sound best with carbon batteries anyways, its not too difficult to put into a rig, since you don't have to run power to them etc. Just plug into the fuzz, then plug into the Axe. Go to the Plexi 100 model, step on the fuzz, roll your volume knob to the "sweet spot" and its a glorious thing! Fuzz face into cranked 100 watt Marshall. Bell bottoms, afro, and godly playing chops not included LOL