We use Mattermost (self hosted) in a team of 30 people with about 20 channels.
On my medium performance phone (Xperia Z3) it can take quite a while (~20 seconds) from tapping a notification to showing the actual message, even in ok network conditions (WiFi or 3G+).
In the Desktop App, there's no such lags.

I'd guess that by having the App run a background service which already fetches the text data for the channel triggering the notification could considerably speed up this use case.