They would go aground regardless whether they were hand steering or the AP was steering to a compass heading or the AP was fully integrated.

Our chartplotter "runs" a zoomed-in course and notes all dangers at the push of a button. Regardless, I always check manually before committing a route.

These discussions are always humorous because there is the full range of opinions of what is "safe" ranging from nothing but DR and paper charts, through only using GPS for lat/long and plotting from that, to fully integrated suites.

Right now, probably the largest popular opinion is that full integration is dangerous. These are the same people who just a while ago were saying that relying on loran and simple GPS was dangerous - but they have been weened up now to chartplotters are OK, but not if integrated.

I bet in the old days people made mistakes with sextants too. In fact, I remember when a celestial calculator came out and people were wringing their hands about the danger of not checking math by hand and using large books of reduction tables.

The more things change...

Mark