I will fall in with the "not worth it" crowd.
If the beer has been lagering for a while, the yeast are likely very dormant and would likely take a while (longer than between now and next weekend) to revive and eat the sugar you are adding. By then, you will likely have suffered oxidation damage from 2 fronts:
1: air entering the headspace, bringing oxygen with it
2: the water in which you dissolve your gypsum solution will have oxygen dissolved in it unless you take care to deoxygenate it, and that will diffuse throughout your beer.
Also, if they don't eat it by then, you will have a sweeter than intended beer.
You will lose a little carbonation not as a result of it off-gassing while the cap is off, but because once you close it back up it will have to off-gas in order to build up an equilibrium pressure in the headspace. When you release the headspace pressure, the beer has to repressurize it by sacrificing dissolved CO2 (and trading it for the oxygen you introduced into the headspace).
Do you really think a little gypsum will help it? have you tried it with a test beer (drink it without, add some gypsum and taste it again)?
Edit: I see you already answered the last question.