Yeah they will take turns on it. It'll probably be so easy for them to flip that switch eventually - and remember: It's not being dishonest if you don't care to correct them. So they did not LIE, they simply did not rewrite the view people had of them. Then they're so good at pretending that when the real thing ends up beginning to happen they're both surprised. 

I don't think anyone in Konoha would be able to assume that until something big happens, like Sakura holding his hand down a market street and shopping with him. I'll admit I came up with the funny idea of someone seeing them in Konoha and remembering them from the town they're in and how they're a couple, and then loudly asking them how they're getting along being young lovers, and then people hear it, and then Kakashi starts sweating SUPER BADLY cause they were playing with fire and now its burning them xD and makes it worse if Sakura's parents are around xD