I think in general, no. You basically start "fresh" whenever you start a new generation.

BUT!!! It seems to me (and it may just be the luck of the draw) that if you praise a kid for "playing office", "playing in the workshop" or "playing cook", they seem to be more likely to have that career.

I haven't really tested this out, but the few times I've praised a kid for that kind of behavior, that was the career that they got.