Would it be better to remove the slats before laying the plywood down?
No. If your rafters are big enough, the extra weight really makes no difference. If your rafters are undersized (as often the case with older houses) you would likely be advised to beef up the rafters rather than try to remove the slats. How do you know if the rafters are undersized? Guess, get an experienced contractor to tell you if they match the typical size he puts in for a given span, or hire an architect/structural engineer ( in increasing order of liklihood of good advice.)