Just going on a few people I know - a traumatic childhood made them very "driven" and they have been very high achievers, although with a lot of difficulty and suffering in their personal life.

You might expect to see the opposite of course e.g. that it would be harder for an abused child to concentrate on reading or schoolwork.

An interesting and possibly related question seems to be the one about nature v nurture, e.g. is intelligence or potential primarily a genetic thing which is then influenced by our environment, or do people start more as "blank slates"...