Yes, it is technically possible to do it with an audio codec (like the CS4272 or AD1835) that you mentioned.
During the development of the pedal-pi with experimented with that option but in the end, we went for a "simpler" ADC (like the MCP3202) because all the codecs in the market are SMD and not easy to solder and for most of the DIYers is not easy to do.
We only use through-hole parts in the projects so people don't get frustrated.
So summarising, yes you can do it but you will also need to do some software development, although I am sure that there are some libraries out there ready to be used.
