Yes you can use Schedule Manager.
Build a QueryTool query with criteria that creates a data result set and use this query on the Scheduled Task. The resulting action would be an "Add Reminder" to the Manager.
Note however this would generate an email for each request returned in the result set. Great if you want to for example if you want to email each raise user independently as a "chase" feature but not so good for manager alerts if more than a few each day unless you want separate ones of course.
Perhaps better is to create a scheduled report (QueryTool query) in Schedule Manager so that the Manager just gets one report per day of those exceeding the time boundaries.