I hope so. That's what i do. I hear the water softener takes out calcium and magnesium and replaces it with salts. You'll be better off using the water before the softener, otherwise you'll just be spending money putting those elements back in.
I also have a water softener at home, and in the morning, what I do is go down to my water softener unit, and bypass it (there should be a valve/button like thing to push to bypass the softener). Then I just use the water as normal during the day to get some hard water back into the system before I do my normal water changes.
I too have well water, no softener, with very similar hardness values to yours and I use it straight, and my plants are doing fine. Some plants you might not be able to grow well, Toninas and such, but there's plenty others to choose from.