No, you are not going to want to set the pump up that way. Change the logic so the pump draws and returns to the bottom of the tank, rather than drawing from the top. Too much pipe for a small pump, especially choking the intake with 1/2 pipe, which is called "restricting the pump intake." Since your output line will be larger than the intake line, the pump WILL cavitate itself into component parts: impeller erosion, and possibly a bent main shaft.
As it is: the head on the pump will be ~double the water level difference between the the first section and the last section, plus the friction loss in the intake line. Not a very good way to install a pump. The pressure differential in the volute, will make the water "boil," e.g. hit its vapor pressure, and the pump will tear itself apart.
I don't pretend to know why you want to re-invent the wheel, (e.g. calcium reactor.) Generally folks are using a salt mix with an unnaturally high level of calcium (hyped so called "Reef Salt") to start with, and a calcium reactor simply drives it higher while alkalinity stays level or falls off, to the point it causes problems.