Will sharrows reduce the chances of getting doored? The best place to look, one study found, is in Chicago, where the city actually examined the extent of dooring in 2010. The study was just accepted for publication this year, though.
One reason for sharrows is to encourage cyclists to move out of dooring range. The researchers compared crash data on Chicago streets with sharrows to those on streets with marked bike lanes and those with nothing special for bikes.
Sharrows didn't seem to help much. The authors realize they couldn't determine why, but found areas “that had sharrows installed experienced less than desirable safety outcomes….” They couldn't say why for sure but suggest that sharrows may “provide a false sense of security to bicyclists” since bike lanes provide dedicated space and cyclists know to look out if there's no marking. Sharrows may also attract inexperienced cyclists.
See N.N. Ferenchak, W.E. Marshall, Advancing Healthy Cities Through Safer Cycling: An Examination of Shared Lane Markings, International Journal of Transportation Science and Technology (2019), doi: https://doi.org/10.1016/j.ijtst.2018.12.003