Whitespace depends on the context. For example, you could have characters that are not counted as whitespace in Unicode, but end up rendering as whitespace when displayed in a particular context. The only real way to check for this is to actually try to render it and see what happens. There are some other ways to approximate it, like checking the font that you use for rendering, or the bounds of the glyph, or other things like that, but the only way to really know for sure in all cases is to just render it and see what happens.
I don't think you can "just render it" to figure out it's whitespace?
As the section "What is whitespace, anyway?" points out, if you render an OGHAM SPACE MARK in a font with a stemline you'll get a visible horizontal line.
My tab renders as: " > ". I still consider it whitespace.
What turns into whitespace due to rendering? Just because my font lacks that symbol doesn't mean it is whitespace.