Lee’s original plan of action for the Gettysburg Campaign was to gain supplies (and allow them to be drawn from areas of Virginia freed from the fighting), and to force the Army of the Potomac to distribute itself across a broad area trying to keep up with him. He thought that once this happened, he could assemble his army together faster and proceed to defeat the Army of the Potomac in detail.
The action of July 1st was pretty close to Lee’s original design - routing I and XI Corps in succession - but the night gave the Army of the Potomac time to assemble. Once it had assembled itself, as was true by July 2nd, Lee had little chance of pulling off his original design. One truism of Civil War combat is that it damaged and disorganized the victor almost as much as the vanquished. Given that the Union was more together than the Confederates on the battlefield (Pickett was still not yet on the field), Lee should have rethought things - as it was, he came closer to victory than could be expected.
If the Army of the Potomac loses on July 2nd, it most likely falls back to the south and east, covering Washington. Lee still has some basic logistic problems. He’ll have a hard time feeding his army if he keeps it together, whether it is on the move or (worse yet) stationary; he also has to worry about ammunition supply, and he has a lot of wounded soldiers to send south on every wagon his army can dig up.
Lee also had a great deal of respect for Meade - he had declared only a few days earlier that the general “would make no blunder on my front, and if I make one, he will make haste to take advantage of it.” Would this retreat have convinced Lee that Meade was, in fact, a blunderer? Or would he have assumed that Meade had been hard done by a subordinate’s error? Considering Sickle’s advance into the Peach Orchard, he might well have assumed the latter.
Given the situation, Lee’s respect for Meade, and the imperative to keep the Army of Northern Virginia alive and fighting, I could not see Lee advancing into a potential trap. More likely, I think he could have maintained a presence astride the B&O main line in Maryland west of Frederick, or possibly as far east as the line of the Monocacy River, reestablished his lines of supply, and kept pressure on the Administration. Feeding his army would not have been easy in this advanced position, but trains run up to Manassas Junction could transfer to a wagon road through Leesburg and to Frederick. (If they could retake Alexandria, they could run trains straight to Leesburg, but the Arlington Line of fortifications had mostly been built by mid-1863 and would probably make the cost of such an effort prohibitive).