Not quite. Going back to the bottling example, a bottle has to be filled, capped, then labeled. At time 1, 1 bottle is filling up, pipeline is advanced. At time 2, bottle 2 is filling up, bottle 1 is being capped, pipeline is advanced. At time 3, bottle 3 is filling up, bottle 2 is being capped, and bottle 1 is being labeled. At time 4, bottle 1 is done. Each bottle has to go through the pipeline in sequence, and it takes three units of time for a bottle to go through the pipeline. Yes, once the pipeline is filled up, you have the three operations going on at the same time, but it's still a sequence of steps that need to be performed in order for any given bottle.
To make it faster, you either have to decrease the time for a step (but you will always be capped with the slowest step), or go for parallelism---a separate pipeline (or pipelines). For example, with one pipeline, each step taking 1 unit of time, once the pipeline is filled, will take six units of time to make a six-pack (the first will take longer due to the latency in filling the pipeline). You can make five other pipelines, and then get a six-pack per unit of time (again, after filling all the pipelines).
A single pipeline just makes the output have a predictable latency and time; multiple pipelines give you parallelism.