I've had a fridge with a 5# and 15# CO2 tank inside of it. I've heard varying stories that the CO2 will deplete faster and other such wives tales. I recently moved the CO2 tank outside of the fridge with a side modification (heck, I figured I could fit another keg in its place), and the only difference is the pressure reading for the tank's internal pressure. PV/T=K explains it all.
There should be no difference--mechanical or otherwise--that will adversely affect the tank, regulator, or carbonation of the beer. You may need to adjust the regulator due to the drop in temperature, but that's about it, and it should be expected.
Once the system is set up properly, the magic will happen.