Cold storage is good for lots of things. Batteries supposedly last longer in cold storage. Glues, SMT (surface mount tech) adhesives, lots of chemical compounds, many things last longer in cold storage. Hey, even the bend and glow light sticks will glow longer in the fridge (at least thats what I have been told, havent spent a lot of time in a fridge watching one to prove that).
I have seen posts here where people have wondered if precipitants werent growth in their inks. I dont see any (serious) reasons to not put them in. It may prolong their life if not used right away. And carts can be used over a long period.
I would hope that the manufactures and distributers would move stock quickly and not ship old stock.
The problem I see with storing refilled cartridges in a refrigerator is the humidity is very low. Things dry out in a refrigerator. You would have to keep them in a hermetically sealed container.
I have always stored my ink bottles in the fridge (next to my polymer clay). This is mainly because my fridge is never full, otherwise I would not bother.
I'm not going to mention some of the stuff my wife keeps in there. OK I will. Candles, fragrances, potpourri (had to look that one up, "Mom, this granola tastes OK but it smells funny").
Point is, cold storage helps with lots of things. It just seems it would be beneficial for inks.
I am sure it's OK but I would consider the following - most compounds are less soluble at low temperature as compared to higher temperature. If the dye is near its solubility limit at room temperature, then there's a possibility that it may precipitate out. I don't know what the solubility of these dyes are in the solvent mixture that is used. As long as you don't see anything precipitating out at the bottom of the bottle, I guess you are fine.