Nominal input impedance of a GE-7 appears to be 1Mohm, same as the Axe FX III, so there's something else going on beside buffering if the sound changes with the GE-7 in circuit.
Being a bit more logical, but maybe more complex, I notice the buffer circuit on the GE-7 seems to do a bit of RC filtering. Looks to me like a low pass somewhere a little north of 7 kHz, but my analogue electronics knowledge is a bit rusty. I guess one could always tone match a bypassed GE-7, and run that tone match as a block straight after the input. That really ought to sound the same.
Liam