It's not an analogy, it's a logical fallacy. Keep digging the hole though; it just makes you look more intelligent as you go.
the only fallacy in play is the reductio ad absurdum which in this case simply illustrates the foolishness of the assertion.
unemployment payments do NOT improve the GDP, they cannot, since they are non-productive.
GDP is a foolish measure of economic activity and the economy since it only measures money in motion, and is entirely unrelated to whether that movement is productive or un-productive.
a similar and equally absurd notion in common use in macro economics is the claim that crime increases economic activity, and thus is good for the GDP.
1) when somebody steals your car, your insurance company pays you for the loss (cha-Ching! GDP goes up by that many $'s)
2) you now buy a replacement automobile (Cha-Ching! GDP goes up again)
3) the car theif sells your car to a chop shop (Cha-Cing! now he has dollars to spend!)
4) the chop shop wrench monkeys get paid to take the car apart (Cha-Cing!)
5) those parts are sold (Cha-Ching Cha-Ching Cha-Ching!)
6) and the purchasers of those used parts now have some extra dollars to spend on other shit by paying less for dubious parts on E-Bay (Cha-Ching!)
thus car theft is "good" for the economy as a whole by increasing aggregate demand, despite being entirely NON-Productive.
of course this is all bullshit, since if your car had not been stolen, the insurance company would have kept all that money and either invested it in some shaky land deal, or blown it all on top hats and caviar at their bi-quarterly executive retreat in hawaii.
i could reductio the fuck out of that absurdum by asserting that the economy would benefit greatly if every car in america were stolen tonight and everybody had to go buy a new hooptie.
but that would be retarded.