I stabilize all grape wine. I do not stabilize kits. Also, learning the hard way, if I buy any juice in the future that is a blend I'll cold stabilize that also. I have a wonderful Raspberry Blush bottled that is loaded with wine diamonds.
I would taste the wine and see if it has more bite than you like. You can test for TA and see where it's at, but really cold stabilizing is more of a way to help smooth a wine out. Some wines benefit, while others may take away it's crisp taste. I'm not sure if there is a definite answer.
The problem with not cold stabilizing is getting the wine diamonds later on in the bottles. They cause no harm except for the esthetic's of the wine. A person not knowing this will be hesitant to drink the wine.
I'm doing a Pinot Grigio right now in a fridge that averages about 35 degrees. It's been a week and no diamonds yet. Like Dan said, it might take a few weeks at that temp. Good Luck!!