not quite sure what your asking...
you could of course connect a pedal to the output jacks of the Axoloti...
and if you wanted to, you could hardwire this, by connecting to the RTS pads, behind the jacks.
and/or you could build your own distortion circuit and connect to either RTS or LIN+/- (see codec for details), but you'd still have to build your own mixing if you want stereo dry/wet.
(if you only need mono, you could use one channel as dry the other as wet)
of do you mean inserting prior to the DAC? that's trickier and depends exactly on what you want, but would need additional circuitry and more code to interface it.
(this is because the coded used, adau1961, only provides the 2 channel IO that is used for the main stereo input/output)
... sorry if this doesn't answer your question, but as I said not exactly sure what your after, also what you can do will depend partly on your hardware/software experience.