Well, lets say your car needs/has a battery with a CCA ( cold crank amps ) of 500 amps, roughly. Your battery is a bit old so lets say it's down to 400 CCA. It still starts your car on a cold morning. Now lets get to the device, it has an 8000 ma ( miliamp ) battery, so 80amps, it is also advertised ( i would like to test that claim...but ok if that's what they say ) with a 200a "pulse". You see the difference? 200 vs 400.... to sum up, no, i can't see that device working on a freezing cold December morning.
It would however depend on how "flat" your car battery is, if your starter was turning, but too slow to fire the engine, those extra 200a from that device might be enough.
I would also be cautious about cranking for more than say 5 seconds with one of those connected to your car.