See your point, Christopher. And yep, you can't really speak of a companion defining a Doctor if we haven't really seen them with anyone else. Hence my feeling that really Pertwee/Jo (or Pertwee/UNIT, though then Liz does begin to stake a claim... but as someone who saw late Pertwee but really grew up on the novelisations, Liz really was just a footnote till I saw and loved grotty pirate VHSes of season 7) is the only time you can really say any companion defines their Doctor.
Does Jo define the Third Doctor or his era? In a lot of ways she's a fairly standard companion from the era -- contemporary human female, not anywhere close to an intellectual match for the Doctor, often frightened -- and she didn't embody the UNIT era in the same way Liz or the Brigadier did.
But on a more intangible level, yes, Jo became very important to the Third Doctor. They had a close, loving, father-daughter relationship, and I don't think I'd seen the Doctor show quite so much devotion to anyone since Susan. It really hurt him when she left. So she defined his more compassionate side, his love for humanity and for his friends. Yet he could often be dismissive and condescending toward her, and that illustrated his arrogance, the way he cared for humanity but didn't seem to respect it much. And yet she also showcased the Doctor's own imperfection and vulnerability, because he needed her to save him almost as often as the reverse. (In "The Daemons," Jo Grant singlehandedly saved the world with her love and self-sacrifice, while the Doctor and the Brig were expending futile efforts against heat barriers and animated gargoyles. And it's always annoyed me that she never got so much as a thank-you for it. She's also the only companion I can think of, at least from the classic series, who could resist the Master's hypnosis through sheer willpower.)
So yeah, I guess she does define the Third Doctor in a lot of ways. And you could say she defines that transitional, early-70s era; she was sort of a counterculture hippie type, liberated in principle but still with the vulnerability of companions from an earlier era, yet able to find the strength to overcome that vulnerability and be an invaluable partner.
I've heard it argued that Rose Tyler was a second Jo Grant in a lot of ways. I'm not sure I entirely see it, but I think I get the general idea: the ordinary girl who's elevated through her association with the Doctor and fulfills a greater potential, the deeply emotional companion who wins the profound, if platonic, affection and devotion of a Doctor who might otherwise have been cold, bitter, and aloof.