There are many hardware design issues that would, most probably, stop you from using the Audio Processor as a CPU...
Streaming data from the Audio processor is one thing (Shining Force III Part II) - actually using it as a CPU itself is quite another
Team Andromeda, AM2, Sonic Team and Camelot Software Planning all found ways of reprogramming the Saturn's audio chip to process geometry or sprite (normally transparency) effects, so it's not that difficult. Of course, these were in-house Japanese departments who received the most up-to-date development kits long before third parties, which may explain why Sega's own titles looked far superior in most cases - especially later on when most other companies had given up on the 32-bit console! However, they didn't always push the system... unless we can forget about The House Of The Dead's terrible conversion for a moment, that is?
The House Of The Dead was converted by Tantalus with only supervision from the original coin-op development team, so does it really count as a first party Saturn game? Come to think of it, why shouldn't we hold Sega responsible for ordering its release without even being properly finished?
The console versions were always used as templates for Sega PC titles, so you can't really complain too much about The House Of The Dead in this respect. However, they could have at least made some improvements, such as those given to Virtua Fighter 2 or Sonic R.