Welcome to the forum!
Most 'jump boxes' have pretty small 12 volt batteries inside
http://www.harborfreight.com/12-volt-jump-start-and-power-supply-38391.html
This one has a 17 Ah battery. Doing the math, that means under the best of circumstances you would get 12 volts @ 17 amps for one hour from the box - In actuality, it won't even do that. Your one hour would provide you with about 200 watts of power (12 volts times 17 amps)
If you used that 200 watts to power a 100% efficient inverter to provide A/C power for the OEM EVSE, it would run it for about . . . . 12 minutes - The 8 amp EVSE uses 960 watts per hour, so 200 watts is about 12 minutes worth of charge time
An 8 amp L1 EVSE charges the car at about 3.5 miles per hour, so your 12 minutes would give you about 1/5th of that - A good bit less than one mile of added range
You could do better by forgetting about the 'jump box' with it's small battery and buying a marine trolling motor battery. If you got one with a 105 AH rating, you would have about six times as much power, so it would run your EVSE for about an hour, giving you the full 3.5 miles of extra range. In actuality though, there are losses everywhere which would reduce that somewhat. No inverter is 100% efficient, the EVSE isn't either and a battery cannot provide 100% of it's rated output more than a few times before it begins to deteriorate
The traction battery under the car weighs several hundred pounds and has a much greater energy density than ordinary lead-acid batteries, so any auxiliary battery which would add even 10 or 15 miles of extra range is going to be either heavy or very expensive . . . . likely, both
Don