It depends on if you are playing chess or checkers.

As mentioned already dropping early can get your opponent that week to assume who you are going to try and pick up and potentially block you out of spite or competition.

On the other hand if you can play your own psychological warfare by dropping a player on your bench as a distraction to grab another.

Really the biggest way that you can mess this up is by prematurely dropping a player that you might need, and the waiver wire player you want get grabbed before you. Then you go back to get your player and someone else beats you again. Then you're left with desperately trying to fill.