Yes you can send with an Axe FX one set of outputs to the board, with full modelling and speakers IRs, and via another set of outputs through a power amp and guitar cab without the speaker modelling.
Some prefer to go that route, but as pointed out earlier then what you hear on stage will differ to what the audience hears. But if it works for you then it's an option.
If you want however to go to front of house and have your own FRFR system on stage probably the most preferred choices are Atomic CLR monitors, or the Matrix amplification options.
@Mayfly, congratulations on the AX8. :icon_thumright:
I am currently on a waiting list for an FX8 for the second time. Long story, but if only there were proper time estimates.