I don’t think so. I don’t see why they couldn’t be but there is nothing right now that would put them there.
The notifications are wholly handled by the cloud connector add-on, myopenhab.org service, and the phone apps. There isn’t anything in openHAB core that actually knows about the notifications. So someone would have to set up some sort of registry or REST API in the add-on, the add-on would have to keep track of the notifications, and then make modifications to MainUI to query for and display the notifications if and only if the cloud connector add-on is actually installed.
It’s a big lift but not impossible.
In the mean time, myopenhab.org has a place where you can see the most recent notifications.
It saves the last two weeks worth of notifications.
Most of us add widgets to our Overview page that only show when there is an alert. For example Battery Level Status or Service Status Standalone Widget
When something occurred important enough to send an alert, it’s usually important enough to display on the Overview page too. Visibility can be used to hide it when nothing’s wrong.