Checking in earlier will only make a minor difference. Your initial upgrade request will cover you until the gate list is used. And once you check in you will be on the Gate list which is not used until boarding has started. As long as your check-in is prior to the check-in cutoff, you will be on the Gate list before it is used. The only advantage of checking-in earlier is for the final tie-breaker (after status and fare class). So the earlier check-in only matters if someone else of the same status and same fare class checks in earlier.

Note it is not actually check-in time that is used but rather check-in sequence number.

But there is no harm in doing the double check-in, but beleive your check-in time (sequence number) will be reset to the later time as the agent will have to cancel your original check-in. So you will be on the gate list based on the airport check-in time -- so the earlier check-in did nothing useful.