They really are very, very different. Knowledge of one helps with the other, but it's far more than just "a couple of weeks to adjust to the accent", for example.
EDIT: It's worth noting that this is mostly a spoken thing, AIUI - most formal/semi-formal writing would be in Hochdetusch rather than a local dialect.
EDIT: It's worth noting that this is mostly a spoken thing, AIUI - most formal/semi-formal writing would be in Hochdetusch rather than a local dialect.