If this was my beer, I would do the following.
Take a gravity reading to see what the gravity is. It may be that you don't need to add 1 gallon. I guess that would depend if you are more concerned with the original gravity of the beer than the volume.
Either way, I would add the water now. I would think it would be less likely to pose an infection risk and you don't have to worry about mixing later and possibly churning up the trub. Plus you would have a true OG and FG for your beer.
I'm guessing it is not a big deal to add the water at the end especially if you bottle your beer. You could boil 1 gallon of water to dissolve the priming sugar. You would not have a true final gravity and would have to calculate it.