Can live chat messages have push notifications to a web-view flutter app?

I have a Wordpress backend that I want to add the Sendbird support chat service to, but for mobile this is connected to a webview flutter app. I need the messages and responses from support to show up as a push notification for my user if they are not inside of the web-view app. This would complete our implementation of asynchronous support messaging for our customers.

Is this possible with a flutter webview app?