to be fair the audio will most probably be fine coming out of those speaker connections....
by the looks of it...
there is an on board amp, most probably something similar (if not the same) to a PAM8403
its just you'll then have to trying adding the volume wheel after that speaker connection....
and then the headphone socket and then the speakers again....
this is where it might start to sound a little distorted.....
you could try using the on-board headphone....
de soldering it and remounting/positioning it where you want it in your build....
but your still need to come up with a solution to add in a volume wheel....
again....
personally i feel/think....
just ignore the on-board amp and speaker out setup....
and just wire/connect directly from the headphone socket
on-board headphone socket
Volume wheel
Headphone socket (for your build)
Amp
Speakers
the only additional thing is the amp, which is only about the size of a penny....
if it weren't for the volume wheel, you could just use the on-board setup....
its the volume wheel that's gonna give you the distortion in the setup.....
having it after the speakers means that the headphone socket wont be controlled by it
as you gonna be trying to connect something that's already being powered by an amp the +/- speaker outputs (for the two speakers) might also give you a headache
you could scrap the volume wheel, and use that opening for the SD card....
(but that opening was meant for a volume wheel)
.