Just adds a nice flavor! If you are hot smoking you do not need to brine the fish as such, just rub on some salt and sugar if using and let it sit for half an hour before smoking. A hot smoke should take no more than half an hour a cold smoke can take up to 24 hours, but probably more likely 8 hours or so. If smoking to preserve then the fish should be very well air dried after brining before smoking.
The sugar in my view really makes the fish taste good, I find if I do not use sugar the fish tastes only of the bitter salt and smoke, but with the sugar the salty smokey flavor is much improved. It goes very well with a single Malt!
As usual it is all down to taste, if you like your fish done without sugar, go for it!
All the best.
Mike