Yes, that'll work.
Calcium Chloride gets quite hot when it dissolves in water. I usually don't dissolve more than 1kg of CaCl₂ in a 10l bucket of water so that it doesn't get too hot. Some prefer to add it straight to the pool for that reason, but I prefer pre-dissolving.
Make sure that you turn off the SWG when adding NaCl or CaCl₂. Let the pump running and turn the SWG back on when everything is well mixed in.
Keep in mind that the 125ppm CH of your fill water can be enough to let the pool CH slowly creep up in summer when topping up evaporated water (Ca doesn't evaporate with the water and stays behind) with fill water that contains calcium. It really depends on how much evaporation losses versus rain (with subsequent draining when the pool overfills) you get.