No, the Republic is well and truly devastating the Empire right now, it is stated outright, the Empire is in chaos because Sith are killing each other in power plays left right and center.
OK here goes.
Remember the timeline stuff? Remember how much the Empire was dominating? I don't think that a few victories for the Republic can counter all that.
I'd bet that the Empire has more raw numbers, more supplies, and stuff.
Yes the Empire ain't doing so great right now, but they're just experiencing a recession. They'll be back (although I'm totally rooting for the good guys).
As for the encyclopedia, I'm sure you're right. But did it say that the Republic was actually doing better and winning the war? Or did it just say that the Sith weren't doing so hot at the moment?