No, states can approve a filed return before the Federal is approved by the IRS.
Yes, the delay of refunds due to the Earned Income Credit and Additional Child Tax Credit only applies to the release of the refund. The returns should still be processed as normal.
Note: E-filed state returns will not be accepted until your Federal return is accepted. This is the first step to e-filing, approval is after the return is processed by the government(s).