Can we change the SortOrder of DBQueue Processor task? If yes, then is it recommended?
This is possible. It really depends on what the task is, and what the reason for this would be? For example, if this particular task is holding up other tasks, or is in a "Is Reset" state, then perhaps there are other issues, e.g. frozen job queue process.
A good place to start would be the database journal. What is it reporting?