Being an ethics professor myself, I didn’t need a study to tell me this!
Oddly, however, we found no relationship whatsoever between professors’ expressed attitudes about the morality of consistently responding to undergraduate emails and their actual behavior. 83.0% of professors said it was morally bad not consistently to respond to undergraduate emails, but these professors were no more likely to respond to our emails than were the 17.0% who said it was morally okay not to respond. In fact, 65.5% of those who said it was okay not to respond consistently to undergraduate emails responded to our second email, compared to only 55.3% of those who said it was bad not to respond. (This was within the range of chance variation given the smallish numbers involved in this particular set of conditions, but the 95% confidence interval for the difference in response rates tops out at a 3.2% advantage for those who think it is morally bad not to respond — so at best they’re responding at practically the same rate.)
On none of these measures did ethicists appear to respond or behave any differently, or any more or less self-consistently, than the non-ethicist philosophers or the comparison group of non-philosophers.