Surely you can only have a comma it you are introducing someone unknown.Almost certainly there should be a comma after old.
In Liverpool, they were joined by a seventeen-year-old, James Teit, ...
Otherwise it is perfectly OK.
It can't be incorrect, but in what way do you think it could be confusing?
Hexane, I think I see what you mean. It would sound more normal to say "...by seventeen-year-old James..." However, the writer/speaker could mean "a 17-year-old James Teit" as opposed to a 19-year-old one, implying that normally people know/knew James Teit at a different age. Do you think the writer/speaker could have been making that distinction?
Ah, but "young" cannot be understood as a noun; "seventeen-year-old" can. There is nothing at all wrong with "They were joined by a seventeen-year-old, Winston Churchill."Surely you can only have a comma it you are introducing someone unknown.
Otherwise, by your logic you would have to write "They were joined by a young, Winston Churchill."