Continuing to hopefully a landing seems a little more sensible to me than bumbling off, still single pilot, to who know's where. The dual autopilot approach is a very safe and low workload procedure. Sure if a go-around needs to be made then do it, but my company don't have a particular SOP on this that I can recall, and in the sim I always try and continue to a landing if possible, even suggesting that you could break minimums to do so if you feel the sutuation requires it. Worrying about go-arounds, fuel, diversions etc is the last thing you need when single-pilot, and I'm sure the poor Captain wouldnt thank you for flying him around with a hear-attack longer than necessary.