According to my research and test, the Distribution group itself cannot implement the OOF function, because it is only responsible for distributing the received mail to all members in the group. So you could create a new mailbox and add it to distribution group, then create an Inbox rule for this mailbox, when receives an email from the distribution group, it will send an automatic reply email. But it should be noted that in order to have the rule send automatic replies to your email messages while you're gone, you must leave Outlook running.
About how to create the inbox rule you could refer to: Use rules to create an out of office message
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