Need advise on stamp paper date

No, the agreement date cannot be prior to the stamp paper's date. Though this may happen in the following cases: -

1. Where a verbal agreement was executed earlier and now the parties wanted it to be coded in written form. This agreement may be given a retrospective efect.

2. Where there was an earlier agreement, and either of the party infringes any clauses therein, in order to settle the disputes, the other party accepts some other lower or part consideration different from the earlier considerations. 

Not necessary, if both the parties admit the facts.

If either of the party disconsent, then there is a problem.