You aren't checked in until you click the "finish" button. So someone looking at seat maps will be behind someone else who just clicks straight through. Then again, if the point is to change seats then it doesn't really matter what your SEQ is since you'll have actually made the seat change you want.

As for which means is fastest to search for the reservation, the PNR or OP number cannot be more than a few milliseconds apart.

In most cases the auto check-in is faster than manual.