I think any native speaker (at least in America) is going to interpret quickie as a brief sexual act. Only if there's a clear progression of context can it be used and understood without the sexual connotation.
For instance, somebody might refer to something as having been a quickie (break, nap, task, etc) but even still there's the underlying reference to the sexual definition.
I don't believe I've ever heard or used the term without it referring to the sexual act.
Perhaps this is just another one of those differences in regional usage?
I'll always remember the time our new office clerk (who happened to be British) asked our boss (quite loudly, in the main room, where everybody could hear) if he had anymore 'rubbers' because his old one was broken. She couldn't understand why the entire staff burst out laughing, until the red-faced boss final stammered out "I think you mean eraser".
I had the same reaction when I read N2G's original sentence.