The FAR is silent on this specific matter, but there are instances when signatures are required with some sense of urgency.  For example, when regarding certified cost and pricing data,  "you should insert the day, month, and year of signing, which should be as close as practicable to the date when the price negotiations were concluded and the contract price was agreed to".   Or, regarding exchanges with industry, "When specific information about a proposed acquisition that would be necessary for the preparation of proposals is disclosed to one or more potential offerors, that information must be made available to the public as soon as practicable, but no later than the next general release of information, in order to avoid creating an unfair competitive advantage."

The use of the word "practicable" sprinkled throughout the FAR means to take action as soon as possible after an event.   Another example would be  "To the maximum extent practicable, the debriefing should occur within 5 days after receipt of the written request."   In practice, and theory, the Contracting Officer should sign the contract, to the maximum extent practicable,  on or before the effective date of the contract. 

 You asked "Is it acceptable for the signature to be later than the effectrive date?" Acceptable yes, recommended no.   

If there was a delay in signing and performance had already begun, you can imagine the difficulties with resolution or compensation if an event occurrred in the absence of a signed agreement.  As noted in prior AAP questions, intent would be the first basis of resolution.  The contract should contain the date of the period of performance, and contain dated supporting documents like the PWS.  Those will help determine what was the governments intent to begin performance, if there is a significant gap between the KO's signing and the effective date.