Perhaps not with this ratio, but something like this with a quartz movement, with the right ratios should be able to advance a "day of year hand" around the fac

Perhaps not with this ratio, but something like this with a quartz movement, with the right ratios should be able to advance a "day of year hand" around the face of a clock. If you wanted to get really fancy, advance a DoY-hand for Venus, Mars, Jupiter, as well as the Earth's.