What an interesting topic and one I’ve given some thought. I’m of the opinion that our style is apparent from writing day one, much the same as our earlier voice day one. Both will be improved by learning, but the basics are fixed.
If that is true, then there is a simple way to convince ourselves, and right here on this forum.
Supposing we read the last 30 or so consecutive posts from any member, perhaps ignoring the odd one-liner, would we have a rough idea of that person’s writing style?
My contention is that we would, depending on our reading tastes. I’m often entertained by just a few paragraphs of flowing, effortless writing, while I’m not so impressed by over-embroidered, halting prose, nor a staccato style that is jarring to read.
Such a test is probably too short, but that assumption would imply that posters are able to hide their true style, persistently; and why should they on a writing forum?
I’m not mentioning names in case it starts WW3.