I'm no expert and don't know if that is a serious issue (the board doesn't seem in very good condition overall)
Aside from the capacitor leakage, the rest of the board is in good condition, if a little dusty.
or if maybe good cleaning and, of course, new caps would be enough to get it up and running again.
I'm 100% sure the only problem with the audio is the capacitors. Last time i had the outputs hooked up to an amplifier, you could still hear the sound but it was really really quiet. Its a very common fault on the a4000.
Edit: with the exception of audio the Amiga supposedly works (there is also a picture in the listing documenting that).
Yes, the Amiga is fully functional otherwise, and has a genuine Kickstart 3.1 and Buster 11.