From my understanding and experience, yes. Even if you put it in the fridge but decide that you want it to ferment longer, you can. Just keep in mind that it will take it a bit to warm up to room temperature and to ferment to the point you want it to.
I recently had to experiment with this because half of my F2's didn't fizz at all. I left them for like 2 days, opened them, and there was absolutely no pop, it was like I opened a bottle of water. I added some more sugar to them and left them for another 2 days, and 2 of them did get a lot of fizz, but the rest did not. I am not sure what I did wrong here, but I can say that it works, even though half of the ones I added sugar to didn't fizz, the other half did! So it does in fact work!
Also, at that point, I didn't care to measure how much extra sugar I put in, I just poured a little bit in each bottle.
Yes you definitely can, I have done this with fruit flavored F2 that I thought was done, but upon opening I learned that it wasn't. Since it was still pretty sweet I didn't add any more sugar, I just left it out for about another 2 days, and then opened it and it was more carbonated than it was the first time.
I would think that if you didn't add more sugar and there wasn't that much sugar in it anymore like there was in my case, then it would become more acidic. But as long as there is either already sugar still in it, or you add more sugar, I don't think it will become more acidic than if you would have just left it out without putting it in the fridge in between.
