This may have been at least a partial explaination of why Meade delayed his pursuit of Lee after Gettysburg. While Meade and Halleck would not have been aware of this second request for Beauregard to move north, they were most certainly aware of the possibility of such from the captured dispatch from Davis, they did have.

Again they (Meade and Halleck) would be thinking this dispatch they had captured was misdirection/misinformation, on Davis' part, in his refusal to commit Beauregard. This would have had the effect of locking Meade in place until this possibility was at least verified, one way or the other. Most military men are by nature conservative in their planning. Very few are as bold and daring as Lee.

This is interesting in that I can see Davis, in his conventional thinking, not wanting to commit his Richmond covering force, in Beauregard, to Lee. Remembering that Davis had insisted that Lee leave one of his largest brigades, Jenkin's Brigade from Hood's Division, Longstreet's Corps, behind to guard Richmond also. One has to wonder, what would have happened if Hood's division battlelines had been extended one more brigade front length to the right, at Little Round Top on July 2nd. Or for that matter one more Division lenght had Pickett division been on the field on July 2nd, and both Jenkin's Brigade and Picketts division taken part in Longstreets attack of July 2nd.

But on the other hand, Lee's request for Beauregards force demonstrates Lee's willingness to commit all available force and holding nothing back. While Beauregard may have never became engaged, had his (Beauregard) force been moved to Culpepper, the implication of his force being in that area could have certainly influenced the outcome of the Battle of Gettysburg.