If you don't mind... when the engine is off and it and the radiator are both cooled down... remove the radiator cap and inspect inside for what looks like a brown pudding emulsion. If you find anything like this... check your coolant reservoir for the presence of this same brown discoloration... it should only appear orange in color. If it is brown and darkening... then more troubles are at hand.
The reason I suggest this is that if your engine suffered from a head gasket failure and coolant leaked into the cylinders... upon combustion... it produces a pure white cloud of exhaust smoke that gives ample evidence of the gasket failure. If your exhaust adjacent the underside of the vehicle was leaking ...the white smoke could escape from such places in this manner and with the wind blowing it about and sending it out under the driver's side of the vehicle.
Unfortunately, a cracked lower radiator hose, a failed thermostat gasket or loosened retention bolts, a fracture or separation in the heater hose and its aluminum line ...or even a crack in the engine block on the drivers side could also evince leaking coolant steam from time to time depending upon varying thermal conditions whenever the motor is either heating up or cooling down. Very low levels of coolant in the radiator might bear out one or the other of these problems if you inspect the areas for any 'steam cleaned' appearances and coolant residues.... or find this damned nuisance brown pudding mud inside of the crankcase.
If you see no evidence of this brown pudding like oil and coolant mixture under the cap or inside the top of the radiator... then there should be no worries about internal engine problems and you should continue seeking the answers to the source of the white smoke as your next course of action.
If you do happen see this goopy brown stuff inside there, then not running the engine before performing a complete oil and oil filter change with an engine flush additive would be the only way to preserve and protect the babbitt surfaces of the bearings inside the engine from being corroded by the coolant and causing the bearings to seize up in the engine if you continue to drive with this junk in there. The engine should not be even be allowed to idle under these conditions.
What happens is that if corroded babbitt surfaces begin to stick to and seize upon the rotating engine components... it will ruin the motor. This brown pudding mixture will have completely destroyed the capacity of the engine oil to lubricate the internal engine parts and will 'gel up' to a consistency that will prevent it from being suctioned into the oil pick up tube in the crankcase and may cause the gerotor oil pump to cavitate and lose its prime.
The chemistry of the coolant dissolving the internal engine bearings takes place regardless of whether the engine is running or not for as long as the coolant is mixed up with the engine oil inside of the oil passages. It should it be flushed from the motor as soon as this action may be done. If you pull the dipstick out and find this stuff on the end and higher up past the fill mark... What follows will be the complications of having to pull the engine head, changing the head gasket and flushing the engine clean of all this mess with multiple oil and filter changes as necessary to salvaging the motor. If God Forbid this problem prevails... many here would recommend performing an engine swap over everything else I mentioned above for the R&R of the engine head.
Well the gas tank is on the driver's side of the truck, and occupies that area. As 
I don't think that "service" was well advised. Have you checked your pressures lately? Most AC systems DO NOT require "a can of r134" as it doesn't get used up in operation. So the question would be what's the history on the "service event"?
Hmm, from the initial post, he said it happened on a cold start, but after putting the truck in gear. I guess we need a time frame there. Was it right after pulling off, or was there a bit of driving first, before the phenomenon?