IMAP, CALDAV and CARDDAV work nearly perfectly for this email client as well. Once again there is one exception, CardDav is read only, as it deletes updated fields on contacts. I reported a different bug to the developers of eM Client and they fixed it within a week, however they have stated that the issues with CardDav is SmarterMail related so they can do nothing about it.
I have reported the bug with CardDav using their bug reporting form. Please do the same for your mentioned issue. Maybe together we can get some support for this fine email client.