Single FMC
Having had some FMC failures on -800s with only single-fmc installed there was never an autopilot disconnect at all. All that happens is LNAV and VNAV disconnect. If this happens during the cruise you will get CWR-roll and ALT HOLD. The Autopilot remains engaged.
The Autothrottle remains engaged but gets no further inputs from the FMC. I believe it will work in CRZ, descent and V/S mode but not in climb. Somehow it doesn't calculate the max N1 values. I'm sorry that I can't back this up with references at the moment.
Just select some basic autopilot/flight director modes like HDG SELECT and you will be perfectly able to fly on autopilot.
Hope this helps,
FC