There's a lot to be said for that. Add to that the results of the first day at Gettysburg.
I know there are historians who put this forward, but that's really not supportable. Nothing in Lee's writings suggests he thought he would be alleviating pressure on Vicksburg. The only thing that comes close was his view that it would prevent reinforcements from being sent to Grant. Lee was hoping to strike a nearly decisive blow that would lead to Lincoln's defeat and the ascendancy of the Peace Party in the North.
"First of all, it would pull the Army of the Potomac out of its fortified lines and disarrange all its plans for a summer offensive in Virginia. That alone would justify a march north. At the same time, it would free Lee of the defensive strictures of the Rappahannock line and allow him to maneuver at will. Once across the Potomac hungry Rebels could feast in a land of plenty, and the ravaged fields and farms of Virginia would have an opportunity for renewal. In the larger scheme of things, Northern morale and will were sure to be shaken by the prospect of a Confederate army--a winning Confederate army--marching into its heartland. 'If successful this year,' Lee had predicted to his wife on April 19, 'next fall there will be a great change in public opinion at the North. The Republicans will be destroyed & I think the friends of peace will become so strong as that the next administration will go in on that basis.' A successful campaign in Pennsylvania--even the army's simply remaining there for some length of time--ought to give voice to the Northern peace movement. And a success there might even impress the European powers sufficiently to push them toward intervention or at least mediation. However he made the case, nothing in Lee's correspondence or recollections suggests that he raised any hopes among his listeners that by marching into Pennsylvania he would pry Grant loose from Vicksburg. The argument that time and distance precluded the Confederates from sending reinforcements to Vicksburg that spring surely applied in the reverse direction to the Federals. In any case, it was too much to expect that the threat of a Confederate invasion of the North would paralyze Yankee efforts on every other war front. It was possible that an invasion would prevent the Yankees from sending (as Lee put it) 'troops designed to operate against other parts of the country,' but that was the most that could be hoped for." [Stephen W. Sears, Gettysburg, pp. 14-15]