My question is regarding how usefull a sump pump installation would be regarding the situation below.

A crack in the wall has been epoxied, and the entire wall has had a "tar membrane" according to the previous owner. The guttering, downspouts, and grade are all good to go, but with a couple weekends of steady rain, we still get water in our finished basement. Curiously, the previous owner said he never had leak/water problems in the basement... hmmmmm.... anyways....

We would only have the pit dug, the sump pump installed, and the outgoing water will be sent to the downspout outside.

Would this be a waste of time/money if we don't dig around the house to pipe in water from the sides of the walls? Would the sump pump help relieve the water pressure from the sides of the walls, and the same for future rains? Or would it still come in through the wall/floor joint since the sump pump would only be for what is below the floor? The basement wall is cinder block.