From what I have read, researchers really don't know what the long term effect on surrounding grass and ornamentals is. Also the dosage amount is speculation, too little and the ground ivy laughs at you, too much and the neighboring grass and plants are adversely affected for months possibly years until the Boron (main ingredient in Borax) has dissipated from the soil. If the soil is too wet/dry/warm/cold all affect the outcome too. All plants need Boron but in minute quantities so finding the right amount to safely use on your lawn/garden area is imperative. Since each part of the country has different weather/soil/humidity conditions the results will be different too. You could call your local county extension office or the University of Ohio and ask if they have any information on using it in your area. Iowa State University and Illinois University both found it could be used effectively under proper conditions and prescribed rates and work. But the University of Wisconsin research results showed it didn't work in their area at all. So pretty much, one gardener could use it and praise it's ability while another gardener in a different location could use it and be haunted by the results for a long time.
Most informative and well written answer Ms. toni. I wish to avoid using any synthetic chemical. I am on a shallow well, and whatever I put on my soil, will be in my water. Many of my neighbors do use chemical's so some of them say I am being overly cautious. They are all 'downstream' in the water table from me though. I shall google boron toxicity and see what comes up.
Borax is used as an insecticide, especially effective to prevent ants and roaches from entering a home. However, it is toxic to some extent to pets, so it is recommended to use the borax in crevices where pets and children won't be able to get at it. It is a mild herbicide, too.