Nope,
Doesn't matter if the CO2 is in the fridge or not.
Storing your CO2 in the fridge will lower the pressure in the tank. From around 600 PSI to maybe something like 400 PSI. **guessing**
Far above the 10-12 PSI you'll pass to the kegs.
FWIW, (I'm a n00b, so ignore me if you want!) I've forced at 30, and I've set it and forgot it.
Force carbing is risky, because if you overshoot your volumes, it's a PITA to get back down to proper carbonation. BUT - I'm not a patient man - I want to drink my beer. There are a TON of opinions here, for and against the practice. But in the end the reality is that force carbing at 30 PSI is nearly impossible to get right. Most of the time you'll miss your target, and sometimes you'll go past it and have to vent it back down. (Suck!)
When I force carb it's because I wanna try my beer! I shoot for less carbonation than what I really want. It's carb'd enough to pull a pint or 2 to get your fix, and still right on the money a few days to a week later at regular serving pressure.