Pushing syrup out of keg?

I was lucky and got a 2.5 gallon diet Pepsi BIB. The box expired a month after I got it. I was able to make it to taste like diet Pepsi from a 2 liter bottle. Well 2 months after I got the box, 1 month past expire it now tastes like gross diet Pepsi from a restaurant. So I'm thinking if I can get another box can I put it in a keg set to 2 psi and just push it out that way? I'm thinking the co2 and the cold with keep the syrup way longer. Ant y info would be great.