I have an idea of monitoring all SQL queries on a spare monitor which is almost not used in my daily coding. You can see latest SQL queries in runtime. Obviously this is not unique.
But I just want to know your opinion on this.
Can this approach be useful? Can it help to detect a problems in your SQL queries faster? Can it help you in understanding a performance issues in your app faster?
Well, you've taken the time to plan it out, and ask a question on SO... Why don't you try it and see if it's useful for you?
That's the only answer that matters.
I have used a similiar set up and would say it can be useful. However I would say it's more useful when you are having an issue (like a query taking too long) and you are looking for this specific issue rather than just always running it. If you are always running it, it may just become noise and nothing specific will stick out.