Hi Matthew,
Currently we’re not able to do that in Office 365. The default OOF setting only works for the Office 365 account.
If you want to send the auto-reply to the sender when a message is delivered to the Office 365 account and the connected account, for a workaround, you can use Outlook to create a custom rule by referring to the links below:
Automatically reply to email messages without using an Exchange Server account (applies to Outlook 2013)
Send Out of Office notices with POP3, IMAP, and Outlook.com accounts (applies to Outlook 2010)
Please note after set the rule in Outlook, it will send an auto reply to each message arrived, for the Rules Wizard to send a reply automatically, Outlook must be running and configured to check periodically for the new arriving messages.