No he wouldn't have. Lee made exactly that assumption when he invaded Maryland and it simply didn't happen. Maryland stayed loyal to the Union. In fact invading Maryland cause many fence sitters in that State to turn their allegiance in favor of the Union.
As for the other "what if?" The previous battles of the Army of the Potomac vs The Army of Northern Virginia in Virginia were never decisive and by that I mean they never resulted in the destruction of either Army as an effective fighting force. There is little evidence to believe that would have happened at Gettysburg cause, as we know, it didn't but for the sake of argument lets say it did. After the Battle of Gettysburg Lee's numerically inferior army suffered over 25,000 casualties. It also consumed most of the ammunition and material supplies and food that the Army of Northern Virginia had. So even if they had won a decisive victory against the Army of The Potomac (which was very unlikely to begin with) the Army of Northern Virginia was still a spent force
that lacked the military force needed to break the encircling fortifications surrounding DC. Also keep in mind the superior lines of communication and transportation that the Union had and that Union forces in the west were the Confederacy was losing badly could have transported large numbers of troops and materials in a short period of time, via the rail roads, as they did during the Chattanooga campaign. That, again, would have inevitably forced the Army of Northern Virginia back into Virginia.
So there is not really a whole lot of basis in fact that this could have happened. The reality is that Lee took an incredibly audacious gamble in invading Pennsylvania, took much needed resources from the Confederate western Armies, and the western theater of the Civil War is where the war was really won, and failed on an epic scale that contributed hugely to the Confederacy losing the war.
The "What if?" I would give you to consider is what if Davis had refused to provide Lee's request for more troops and supplies, ordered him to stay in northern Virginia on the defensive and had provided those recources to Johnston and Pemberton in the west to fight Grants invading army which had taken the extraordinary risk of invading Mississippi while cutting both his lines of supply and communications? What if Davis had ordered Lee to give up additional troops and resources to the Chattanooga campaign which would have at worst delayed the taking of Atlanta to after the 1864 election? Then a negotiated peace would have been far more probable.
With that you can begin to see what I mean about Lee being a very poor strategist.