He is the kind of person who, if he had lived in the 19th century, people would not have been able to categorise him.
This is a rhetorical device known as anacoluthon. The grammatical structure of the sentence shifts as the sentence is spoken — or, you could view it as, two different sentence structures have been smushed together into a single sentence. (Did you notice, I did it there. And (arguably) again!)
The two sentence structures smushed into this one sentence are (with the primary subject/verb in bold):
He is the kind of person who would not have been categorizable by anyone in the 19th century.
If he had lived in the 19th century, people would not have been able to categorize him.
The actual sentence spoken ends up smushing the two grammatical sentences together, typically with a moment of grammatical confusion (indicated by a comma or dash) in the middle.
Wikipedia gives several examples of anacoluthon in English, including Milton's
Had ye been there – for what could that have done?
The two sentence structures smushed up here are
Had ye been there, you could have done something. (Well, actually, no, nothing— never mind.)
It's okay that you weren't there, for what could that have done?
The implication is that the speaker changes his mind halfway through the line.
In your original example, the speaker has not changed his mind about what he wants to say; he's just made a little tweak to how he wants to say it.
For an extreme example — in which the extreme disorder of the words does (well, is implied to) reflect the extreme disorder of ideas behind them — look at Fred Armisen's "Nicholas Fehn" character on Saturday Night Live.
You know, it's— it's the reason... I wake up— I wake up, like, anybody— I was taught... Every— well, most Americans, if you— Education. Any— any border, if Helsinki, if Oslo— I think— any publication, we would— isn't it integral, isn't it the most important— it's the substance, the very idea, that we can unite, that makes me feel, personally—