No, automapping is only supported when you add the permissions directly, not via group. There have been some improvements on this for the new Outlook client, but that one has no support for on-premises Exchange currently.
You can certainly script the process to add permissions based on group membership, if automapping is a must. Something like this should work:
Get-DistributionGroupMember DG@domain.com | ? {$.RecipientTypeDetails -eq "UserMailbox"} | % { Add-MailboxPermission shared@domain.com -User $($.PrimarySmtpAddress) -AccessRights FullAccess }