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In Chinese, there are several different strokes, and they should be written in a specific order. For example, you write a horizontal stroke first, then a vertical stroke. When there are characters that have a rectangle around them, you write three sides of that rectangle first, then what's inside, then the fourth stroke of the rectangle.
To what extent is learning this stroke order perfectly helpful for learning characters?
Short answer: no.
Long answer: no, but it increases overall fluency and will help your legibility.
Chinese (as well as other character-based language systems) can have characters that seem to differ only in the direction of the stroke (like 千 [qiān] vs 干 [gàn]). However, the stroke order is still the same.
When I lived in Taiwan, I would ask natives what the "correct" stroke order was for certain words, but even they did not have a complete consensus on what was "correct". In some cases, they would tell me what the proper stroke order was, but then in the same breath would say that they didn't do it that way.
With that said, there are general rules for which strokes come first, but these may be ignored in some instances if there is a different purpose (such as for poetic or calligraphic value). Overall, it is generally best to be able to read the characters first, and then later learning to write.
This is general to all languages: learning to read (literacy) generally should precede learning to write (or spell). I am a native English speaker, but even I come across words that I know how to pronounce and define, but spelling it is a whole 'nother story. (Can you spell 'onomatopoeia' without looking it up? I had to look it up just now.)
Learning proper stroke order will make your characters look nicer and you will be able to make the characters flow together. (Some Taiwanese natives thought that the letters I wrote them were written by a native Taiwanese high schooler because of how much I practiced writing characters.) In all, it won't necessarily help you learn Chinese, but it will help you write more Chinese-esquely.
This article is an interesting note about literacy in China among younger people.
Learning the stroke order probably does not help with learning the spoken language. However, with regard to the written language, the arguments that come closest to cognitive benefits are related to memorisation (including motor memory) and the ability to recognise characters. See the papers I found below.
A paper by Law et al from 1998 points out that the two traditional arguments for learning the stroke order were:
Law et al came up with a few other arguments for learning the stroke order:
The children in the study by Law et al said that they found stroke sequence important, but this perception conflicted with the stroke order errors they made.
A paper from 2010 by Tian et al claims that a "correct order may bring benefits in both memorizing the shape and crafting a better-looking handwriting" but the authors do not back this up with research.
A study by Chen et al (2013) found that when non-native speakers of Chinese get instruction about radicals (both phonetic and semantic radicals), they perform better than a control group with regard to "radical recognition, semantic radical awareness, and phonetic radical awareness". They also had a better knowledge of stroke order than the control group. (Note: the instruction on radicals included instruction on the stroke order of the radicals.) However, this does not show that learning the stroke order as such is beneficial to learning.
A document by Discover China says that learning to write Chinese characters will help you understand their components (i.e. faster than just reading them or inputting them through pinyin or zhuyin fuhao). However, this does not require that you learn the exact stroke order.
A paper by Guan et (2011) points out that "the advantage of handwriting may have a sensory-motor source", i.e. handwriting creates a mental model of the characters combined with a motor memory and motor memory can last for a long time. However, it is not clear to me why this motor memory would require the correct stroke order; it can probably be based on any stroke order that you use consistently.
There is also a summary of another study that says that, "All studies confirmed that when the segments of a character (...) were presented out of normal sequence, the subjects took longer to identify the character, or had difficulty identifying the character, or couldn’t identify the character."
PS: To avoid confusion: I am not questioning the usefulness of learning the correct stroke order. I have experienced the effects of sensory motor memory myself. But the studies don't prove that a non-standard stroke order, when used 100% consistently, would not have the same effects. Of course, with a non-standard stroke order, you may experience some disadvantages, e.g. when using a program that supports handwriting recognition, and your handwriting may look worse.
