I believe the short answer is no.
In at least most states, maybe all of them, the state taxes residents on their total annual income, regardless of where it was earned. They also tax nonresidents on income earned in the state, and you can generally get a credit for taxes paid as a nonresident when you file your state tax return in the state in which you are resident.
The fact that once you are a resident a state gets to take you on worldwide income is why New York, for example, will carefully track wealthy taxpayers and jump on them for taxes owed on all income the minute they hit 183 days in state (and they get to round up every partial day to be a complete day).