You can decode the audio bits - it's just Sony's special version of ADPCM - or use a cartridge (for those PlayStations old enough to have a cartridge port) and read out the SPU memory over X-Link. You didn't even need a debug model to do it (although you did need a handy parallel port and the ability to bit-bang, or run a DOS program).
The CODEC used CD-XA Mode 2 Form 2 (2532-byte sector, with less error-correction layers) ADPCM-compressed streaming audio, 1 of 8 channels, at a relatively low sample rate - which works fine for speech. Lots of PlayStation games used the same basic technique for music and voices (as well as FMVs, although the bulk of that data would have been MDEC-compressed video).