I think the answer is more of a "maybe" than a "no." But you need to review the requirements for reporting income by the non-resident state.
In general, income you receive while living or working in state #2 can be taxed by state #2, while all your world-wide income is taxed in your home state. If the 401k withdrawal was made while you were physically living on working in state #2, state #2 might want to try and tax it. It depends on the laws of state #2. (If the withdrawal occurred while you were physically living or working in your home state, it is definitely not taxable by state #2.)
Timing may also matter. It may make a difference if you were in state #2 for two weeks or 9 months, for example. You need to look at the laws for state #2.
