This could be interesting, but survival rate could be very low. Since these are cuttings, with no roots to store energy or sunlight to create energy, then the cuttings are more like chopped lettuce. It is being semi-preserved by the cold temps in the fridge. Logic tells me that the cutting has about a 5-10% chance of surviving and recovering. I like the idea- really, I'm just not too sure that it can actually make it.
Now if you took a clone that had a decent root system already and pulled it right away and put it into the fridge...that's another story. I will try that with some of my cuttings, some should have roots about 8" long shortly, so it will be a good test. The same principle of stored energy applies to seeds...it is not alive but actually a plant battery...once the water and warmth hit the seed it uses the stored energy within to grow outwards. Cuttings really have no stored energy and would have to scavenge nitrogen from any large leaves to try and survive. If you look at your fresh produce section of most major grocery stores, you can find hydroponically grown basil and such...that still have the roots attached. We have bought this basil, cut some off for our italian dinner (yum)and planted the rest right in the dirt and they are still growing to this day(indoors).
I hope you prove me wrong for your plants sake. Keep us all posted!