Anytime a water softening system is installed any water lines going outside the house should bypass that system, something any compentent installer would do. If your system is not set up that way it can be changed, and the cost will be less than operating your system with softened water going outside.

If not, what affect would the treated water have on the lawn and garden?

Not much, but it would drive your operating costs of your system through the roof. Some people might suggest that the salt in that water would kill your plants, but if your softened water had that much salt in it the water would kill you.

Thanks. We don't drink the the tap water.