Jackson's artillery would've played on the Yankee positions and made them untenable.
I am wondering if this successful escape from a near disaster in 1862 did not contribute to Lee’s over confidence 9 months later some 25 miles to the north at Gettysburg? Memories are a powerful influence upon future actions and this was a perfect example of how the CSA Army of Northern Virginia out thought the USA Army of the Potomac, even at the 1 to 2 odds of available forces.
Of course there were significant differences between the two forces at Gettysburg and Lee erred in mis-accounting for them. Longstreet was not Jackson and Meade was not as pathetic as McClellan. Also significant was how the Union (USA) forces were learning how to fight and to RESPECT Lee’s strategy & tactics. Also, the US Navy was successfully implementing the strangle plan that reduces the CSA’s support. They took the Port Royal Sound / Hilton Head in 1861 and then New Orleans in 1862 from the sea.
If Jackson had not been killed in May, it is a near certainty that he would have been Lee’s ‘Second in Command’ and the endless speculation of what would the advice be on that 3rd day? The charge to the center (Pickett) OR move the ~70 miles towards Washington for better ground? The CSA, in both these campaigns was seeking a “Battle of Saratoga” victory that MIGHT get a foreign alliance and aid for the Confederacy.
Jackson's artillery would've played on the Yankee positions and made them untenable.