From my experience, no. I had 3 on one planet and the ships took exactly the same amount of time.

Although admittedly I haven't actually tried clicking on each individual factory and producing a different unit with each one, so maybe that would have worked, certainly clicking on the planet and building from there didn't make things any faster.

If u have 3 factories, and u queue 9 ships , the progress bar is the same speed but 3 ships pop up the same time (queue counter goes down by 3 each time a progress bar is ended), hence 3 times faster than building 9 ships outta 1 factory.

Yes, multiple factories produce that many more ships for the same amount of time, but you have to remember, if you don't have the econ to actually buy the ships out of three or so factories, then multiple factories are just dead weight. And you will be dead also if someone catches you.

If you see someone overstretching themselves, best strategy is to hit them hard early while their econ sucks. They won't have as many ships as you because they wasted their resources in expansion and building multiple factories. But if you let them develop, then you will be screwed. You have to know when to commit to building up a fleet vs. expansion and turtling, and the only way you can know that is by scouting.