As a friend of mine also wanted to play it, and he seemed to have some problems using WINE, I had a look at it again. I mean, I know my way around wine and the tricks you can use to get things running in WINE.
For the game to detect the CD, the CD drive needs to be set in wine. If the link d:: (or whatever drive it is) points to the CD device it is set. Now we only need to install the libcdaudio library. On 64-bit systems, also install the 32-bit version of the library as well. Now the game should be able to detect the CD in the drive.
While I was tinkering around with WINE, I remembered the game had some nice background music. I was never able to listen to it outside the game: the sound was always garbled. So I tried out several raw import options in Audacity. Only the VOX import functionality seemed to output something that wasn't garbled. Too bad it can only import mono, so the imported audio is still distorted. Giving up now? No, I'll continue.
Looking up the wave format specification, I found out at byte 8 there is a 4-byte field specifying the format. The audio files have 0001 in that field, which stands for 4 bit Microsoft PCM. Looking up VOX pointed me to OKI ADPCM which is one the VOX formats. So I tried out the corresponding value, 0010, and it works. Nice! Finally, I can import the background music of Anno 1602 into my audio library. Now the question is, was that deliberate? I'll never know…
Next, I would like to be able to add own music to Anno 1602. But so far I have not been able to encode files to stereo OKI ADPCM yet. Setting 4-bit Microsoft PCM to the bit-swapped value 0010 doesn't help. If you know how to do that or have the software for that, please do get in touch!
Also, if you want to try it out, you can buy Anno 1602 on GOG.com
EDIT: To properly import the songs in to my library, it would be great to know who composed those songs. It was Markus Pitzer