Well, reading the book I just finished on Vicksburg (The Final Fortress), Pemberton's fear was that his attempt to join Johnston would end in the capture of Vicksburg. Meanwhile, primary sources indicate that Johnston's plan was to strike at Grant's supply base.
Oh I get what you mean now. Still, in order to get to Grant's "supply base" Johnston would still have to battle Grant somewhere around Jackson first. Then he could move on Grant's beachhead on the Mississippi.
Such a plan would not interfere with Grant in the least because he planned to abandon his supply base and live off the land in the interim. Also, in OTL, Grant felt comfortable dispatching Sherman from the siege of Vicksburg to face Johnston alone outside of Jackson (Johnston never arrived). Surely in this scenario, he would possibly attempt the reverse, leaving Sherman to take the weakened defenses of Vicksburg while facing Johnston with his own forces.
Actually that's not entirely true. Grant still had a link with his beachhead, which also acted as a supply depot, at Bruinsburg & Grand Gulf. It is true, though, that he was prepared to move, at times, without letting his supply columns slow him down. The thing is Grant's army, without or without Sherman, still have to secure their rear, meaning Jackson has to be taken. And if it doesn't involve the entire army, but is either divided up, as in the OTL, or as per your scenario, whilst Johnston & Pemberton have united their forces, then the Union should suffer a major defeat as a result of being smaller in number & divided.