I am efiling federal and state. If I efile both at the same time, but don't have the federal deducted until a later date, will the state be efiled on the later date also?

No, making a payment will not refile your tax return(s). You can e-file both returns and pay your federal balance due at a later date. You are not required to pay your balance due on the same date that you file your return(s). Making a payment and e-filing can be separate events. If you have already chosen to e-file both returns and they have both been accepted by the taxing authority, then you have filed them both. 

When your payment is deducted from your account, it will not affect your state return. The federal and state returns are processed separately.