I just looked further into this. It seems that in the set-up here, not Kerberos is used for the mail but NTLM with some special mechanism for single sign on. A package in RHEL/CentOS called gssntlmssp should provide similar support.
On the Microsoft site it can be found that Outlook has specific behavior when it detects that the client is joined to a domain and then queries the domain controller to obtain the right information. See Autodiscover transaction summary. Looking at the output when trying to add a mail account, I noticed this:
fixme:netapi32:NetGetJoinInformation Semi-stub (null) 0x33cb04 0x33cb08
The Microsoft page on NetGetJoinInformation shows that this is used to obtain information on whether the system is joined to a domain or not. In the Wine source code it's visible that variant is not implemented yet.
Hans Leidekker also commented in Wine bug 30765 that Exchange 2013 needs more support. The rest of the output from Wine suggests the same (multiple errors that certain actions are unsupported).
This means that neither single sign on nor Exchange 2013 (which is used here) are currently supported. Using another mail client in combination with DavMail or Evolution will work better for now even if that means you need to store your credentials in them separately (and update them everywhere each time your password changes...). It would be interesting to see what happens with an implementation of NetGetJoinInformation which can return the right status on a system which is in a domain. Maybe I can look into that at some point.