The hard and fast rules are prescriptive, but once you start writing, you realize that some of that prescription ends up as description. There really are detectable orthographic differences in how stroke order affects (generally, of course) how people write.
i have not met anyone who did not learn the chinese language without doing penmanship work, and so i cannot say what it means to ignore the stroke order when writing chinese. if one were to pick up the latin alphabet with an unusual stroke order and were to carry that habit to adulthood, will we find his handwriting difficult to read? if he managed to train his hands to write with a most unusual method will he still write perfectly legibly, and can we even distinguish his stroke order if we were to inspect it carefully? i don't know the answer to this. out of curiousity i wrote the alphabet with a totally unfamiliar stroke order (e.g. starting the y's and g's from the bottom) and it looked as if i wrote it with my off hand - unsteady and unpracticed - which seems to suggest that maybe with some effort it could look totally similar. i can believe that without stroke order guidance one could still achieve legible chinese writing.
It's genuinely hard to read people's writing if the stroke order is off.
If you write super slowly and deliberately it may not matter much, but in my actual real-life usage I've found that it does. If you're learning, you're definitely better off learning the standard stroke order for the area where you live.
I believe there's a reason for the rules and that you need to know them. I think patio11's metaphor is the correct one -- it's a lot like english spelling.
I doubt your last claim in the general case, and I think the GP comment in particular is taking things too far -- there's no way that the average Japanese reader is going to be able to tell the stroke order used to write ぉ (in handwriting scenarios, not calligraphy), so long as you don't mess up the form of the thing.
I also don't buy Emmett's claim. There are regional differences in stroke order, even for hanzi. Japanese people use a different stroke order for kanji than mainland Chinese people use for hanzi, which again is different than the stroke order used by people in Taiwan and Hong Kong. The differences implied by these things are smaller than the differences in CJK fonts, which have no inherent "order" at all, yet people somehow manage to read.
Stroke order matters for calligraphy and memorization and dictionaries, but as patio11 says, it's largely just prescriptive. Spelling is prescriptive, too: it's historically and/or conventionally derived, but knowing the rules makes learning words easier, and you certainly can't use a dictionary without it.