Dictionary lookup is done first by radical and second by stroke count. Collation is not. Stroke count is first.
For example, I have a book of 成语 stories that gives its table of contents in non-alphabetical order. (Since nobody understands the traditional ordering, I also have several such books that put their table of contents in alphabetical order.)
Note that 三's radical is 一, the first Kangxi radical, and that 一 is listed first. Your theory is wrong. 三 isn't even first among the 3-stroke characters, which start (among these) with 口.
Why did you make up a false answer to this question?
For example, I have a book of 成语 stories that gives its table of contents in non-alphabetical order. (Since nobody understands the traditional ordering, I also have several such books that put their table of contents in alphabetical order.)
Here is the collation order in the book:
一 七 八 入 九 人 口 千 小 三 亡 大 不 专 天 井 见 毛 月 文 风 为 心 水 四 ...
Note that 三's radical is 一, the first Kangxi radical, and that 一 is listed first. Your theory is wrong. 三 isn't even first among the 3-stroke characters, which start (among these) with 口.
Why did you make up a false answer to this question?