Following Jackson's death In May '63, Longstreet advocated a western offensive plan (which can be traced back to Jan. 23) to Lee, to consolidate and reinforce Confederate forces (put under Johnston) at Tullahoma, to counter Rosecrans, then advance on Ohio, as a way of relieving Grant's pressure on Vicksburg. (He did not propose directly relieving Vicksburg). But Lee rejected this plan on the grounds that to divide the A of NV (by sending reinforcing divisions from Longstreet's Corps west, as suggested) would be unsafe for facing Hooker's superior numbers in the eastern theater.
In relation to Vicksburg, Lee believed the better option was for Johnston to reinforce Pemberton, without sending reinforcements from the A of NV.
Lee's final decision to maintain the strength of the A of NV was for the purpose of renewing a northern offensive (despite Longstreet opposing such a move). Apparently the rationale for Lee's decision was that he thought his Army could be more effective serving the Confederacy by invading the North and threatening Washington. A factor in Lee's decision may have been the recent loss of arguably his best Corps commander, Jackson, which made him less inclined to reduce his Army strength for the operation.
My reading of these events. Definitely thought Vicksburg was a factor, as an intended indirect outcome, in Longstreet's planning, but not so much in Lee's thinking.
As the war continued with its attritional effects, prominent Southern leaders (like Lee) realized that they could not maintain a protracted defensive strategy, but needed to strike instantly to attempt a decisive victory and hopefully force an immediate peace. Given the macro picture, don't think Vicksburg's status in these circumstances materially affected Lee's decision in May '63 to launch a northern offensive into Pennsylvania.
Bringing the