Yes it is possible to add them to the map, in the projects page select the options (gear symbol) for your project, in that menu open the "Worker Map" and you can edit it as any other web map.
As for making them disappear when the work has been completed that is likely a much more complicated task if it's possible. (My thought involves using some kind of trigger to update a field in the polygon that the symbology or filter is based on. Maybe you could integrate Survey123 and link the assignment to the polygon with an ID? Or use Power Automate/Make to scan for layer changes to update them, but Survey123 is probably easier)
