New App / Widget: Chrono Widget

Sure. All this is based on dates (including time) written to a file.
Basically, you set the timer to one hour, then the goal time is now+1h.
When the widget is loaded, the target time is read again and compared to now. If the difference is <= 0 you get an alert. Only thing is that the widget has to be running to alert. But it does not have to run the whole time, like a timer app.

You could create a setting where reminders should start and write that to the file.
Then after a certain time alert and write the next alerting time to the file.