Yes, the Outlook web client ( Outlook Web App / OWA ) fully supports the Out of Office responses. This is how one can set it up:
1. Login into Outlook Web App.
2. Select the gear icon (Settings) -> See all Outlook settings.
3. Find: Mail > Automatic replies.
4. Toggle on, select your time frame and open/close messages to internal/external senders.
For more read, Visit here – how to setup out of office in outlook