ASRS 2070497

The event occurred while on the RNAV 28 approach into Morey Field (C29). The flight originated from ZZZ under MVFR conditions. I did not file a flight plan. While enroute, ceilings were lower than I expected so I requested, and received, a pop up IFR clearance direct to C29. The flight enroute was uneventful. Upon contact with Madison Approach I requested the RNAV 28 approach into C29 and was told to expect the approach. I received a vector assignment of 050 degrees. At that time I assumed I would receive vectors to the final approach fix and set the GPS (Garmin 530) for vectors to final. I then received an altitude assignment that put me into actual IMC conditions. I was then approved for the RNAV 29 approach via the IAF EXIDE. This was my first time flying in the area and I had to confirm the IAF name. I received a vector to the IAF and while updating the GPS route I entered an unusual attitude. Once I recovered from the unusual attitude I already passed the IAF and instead of flying the appropriate approach via a course reversal I immediately turned inbound which took me out of the protected airspace and close to Madison (MSN). I then continued the approach without incident and cancelled my IFR flight plan in the air.