It depends how long your server was off for, if it was just a short outage then maybe you might get some of the notifications you missed, because when Twitch sends a notification and fails to get a reply from your server it’ll try a few more times with an increasing backoff timer.
If your server was offline for more than just a short outage though, those notifications are lost, Twitch isn’t going to buffer them indefinitely for you just because your server is offline.