I don't think it would matter so much on an old car ,unless it turns out to be stolen A newer car ,it would be a very good idea. There is a lot of flood cars showing up.
I think a car fax only works with newer cars. Every time a newer car is worked on ,or insured .inspected or had a smog check , or has any thing done in a licensed shop it goes on record .An older car may show insurance and registration but probably not much else as most people do the work them selves so there is no record to search.