BeerBorg

Is it necessary to keep the CO2 tank connected to the keg while it sits in the fridge or can I just set the pressure and disconnect the line? I'm not certain I can fit both the keg and the tank in my mini fridge at the same time.

It depends: Are you just storing it in the fridge or serving, too? The CO2 is doing two things:
1) Putting pressure on the beer to force CO2 to the point of equilibrium
2) Pushing the beer out through the beer line

If you carb up, then disconnect the lines you'll use CO2 in the keg to serve the beer and it will soon go flat as the pressure in the keg readjusts. The constant CO2 pressure ensures you stay carbed and can serve.

Just storing for now. I wasn't planning on hooking the tank back up until I start to serve.

If you are carbing it, the tank has to stay hooked up. Pressure will drop as the beer absorbs the CO2. Once the beer is carbed you can remove the tank for as long as you wish. The pressure has no place to go in an air tight container.

Ok, thanks. I'm gonna have to try to make both the keg and the tank fit in that little mini fridge. It shall be done!