I presoaked 1 C of Quaker Old Fashioned grits last weekend, but didn't get a chance to cook them. They have been in the fridge all week in the same water. Is it possible that anything inimical has grown while they were sojourning in their cool bath?
Yes it is indeed possible.
The available starches that have dissolved in the water are a super convenient place for the bacteria that is naturally found on foods to grow.
I'd say for grits 2 days soak is the limit, they can start to fall apart after that.
The ultimate test is the smell test, if it smells sour then it has started to turn. This is how I determine if I have oversoaked legumes or grains (life happens!)
Adding a little vinegar to the water may help prevent this for a couple dozen extra hours, but as you likely realize, soaking for no more than 8-12 hours is the way to go.