That's another interesting question.
To begin, I believe that Vicksburg was of key strategic significance to the Confederacy. The South could not afford to lose this vital transportation hub. In my opinion, its loss was the turning point of the war.
But the question raised here is about Johnston and his intentions.
As previously mentioned, one can get some indication by looking at Johnston's mindset beforehand as theater commander. He did not favor deployments of scattered undermanned commands, instead opting for troop concentrations to fight defensively. His defensive tactics also preferred fighting by skilful maneuverings (his references to a willingness to giving up ground for longer-term gains, implies his preference for defensive mobility).
A further guide as to his possible intentions in the situation can perhaps be found by examining his conduct in actual combat command. In May, 1863, while at Jackson, Johnston (as theater commander) urged Pemberton to combine with him, to attack Sherman's Divisions around Clinton, about 15 miles northwest of Jackson (Johnston, however, did not seriously intend to join up with Pemberton at Vicksburg). When this plan failed to materialize, Johnston and his gathered small force withdrew to Canton, northeast of Jackson.
Similarly, as further guidance of his possible intentions, one only has to look at how he later applied his defensive strategy of skilful maneuverings during the 1864 Atlanta campaign. Richmond came to believe that he would readily give up Atlanta in the pursuit of his own notions of a mobilized defensive strategy, without necessarily committing to securing long-term a fixed position, like Atlanta.
My bottom line opinion. Johnston would not reinforce Vicksburg because it was a fixed position and he saw there a real risk of entrapment. He would also not engage Grant outside of Vicksburg because he could not concentrate enough troops (commands were too dispersed) in the vicinity, during this period. I think if he was appointed to Army command, he would have implemented a more effective defensive strategy than Bragg in middle-Tennessee by the time of the Tullahoma campaign.
I belive that there were enough troops in the area that could be able to help Vicksburg. Also if Richard Taylor had gotten troops then he could have helped protect Port Hudson. Plus I have a way for Johnston to kept the Army of Tennessee in good shape while sending two divisions when needed to help Vicksburg. That way is have the army rebuilt into two Corps under Polk and D.H. Hill with four divisions under each corps and three indepedent brigades at Chattanooga and the department of Eastern Tennessee would be regrouped into the army as well.
Army of Tennessee: General Joseph E. Johnston
Polk's Corps: LtG Leonidas Polk
Cheatham's Division: MG Benjamin F. Cheatham
(1st, 6th, 9th, 27th, 34th and 24th Tennessee Battalion) Maney's Brigade: BG George E. Maney
(12th, 13th, 29th, 47th and 154th Tennessee) Smith's Brigade: BG Preston Smith
(4th, 5th, 19th, 24th, 31st, 33rd and 63rd Tennessee) Strahl's Brigade: BG Otho F. Strahl
Donelson's Division: MG Daniel S. Donelson
(8th, 16th, 38th, 51st, 52nd, 81st and 22nd Tennessee Battalion) Savage's Brigade: BG John Houston Savage
(18th, 32nd, 36th, 38th and 58th Alabama) Clayton's Brigade: BG Henry D. Clayton
(1st Confederate, 37th, 47th, 55th, 65th and 4th Georgia Sharpshooters) Stovall's Brigade: BG Marcellus A. Stovall
Anderson's Division: MG J. Patton Anderson
(19th, 22nd, 25th, 39th, 50th and 17th Alabama Battalion) Deas' Brigade: BG Zachrich C. Deas
(7th, 9th, 10th, 41st, 44th and 9th Mississippi Battalion) Chalmers' Brigade: BG James R. Chalmers
(24th, 27th, 29th, 30th and 34th Mississippi) Walthall's Brigade: BG Edward C. Walthall
Cleburne's Division: MG Patrick R. Cleburne
(2nd, 35th and 48th Tennessee, 1st, 9th, 13th, 15th, 19th and 24th Arkansas) Polk's Brigade: BG Lucius E. Polk
(2nd, 5th, 6th, 7th, 8th and 18th Arkansas) Liddell's Brigade: BG St. John R. Liddell
(16th, 33rd, 41st, 45th and 18th Alabama Battalion) Adams' Brigade: BG Samuel Adams
Hill's Corps: LtG Daniel H. Hill
Breckinridge's Division: MG John C. Breckinridge
(1st, 13th, 16th, 20th, 25th and 14th Louisiana Sharpshooters) Adams' Brigade: BG Daniel W. Adams
(1st Florida Cavalry, 1st, 3rd, 4th, 6th and 7th Florida) Davis' Brigade: BG William George Mackey Davis
(2nd, 4th, 5th, 6th and 9th Kentucky) Trabue's Brigade: BG Robert P. Trabue
Buckner's Division: MG Simon B. Buckner, Sr.
(43rd, 59th, 60th and 23rd Alabama Sharpshooters) Gracie's Brigade: BG Archibald Gracie, Jr.
(1st Regulars, 5th, 32nd and 2nd Georgia Sharpshooters) Jackson's Brigade: BG John K. Jackson
(6th and 10th Texas, 15th, 17th, 18th, 24th and 25th Texas Cavalry) Deshler's Brigade: BG James Deshler
(10th and 19th South Carolina, 24th, 28th, and 34th Alabama) Slaughter's Brigade: BG James E. Slaughter
Stewart's Division: MG Alexander P. Stewart
(2nd, 17th, 21st, 23rd, 25th and 44th Tennessee) Johnson's Brigade: BG Bushrod R. Johnson
(18th, 26th, 28th, 45th and 23rd Tennessee Battalion) Brown's Brigade: BG John C. Brown
(11th, 15th, 20th, 32nd and 37th Tennessee) Bate's Brigade: BG William B. Bate
McCown's Division: MG John P. McCown
(9th Texas, 10th, 14th and 32nd Texas Cavalry) Ector's Brigade: BG Mathew D. Ector
(1st and 2nd Arkansas Rifles, 4th, 25th, 31st and 4th Arkansas Battalion) McNair's Brigade: BG Evander McNair
(29th, 39th, 58th and 60th North Carolina) Vance's Brigade: BG Robert Brank Vance
(1st, 54th, 57th, 63rd and 64th Georgia) Mercer's Independent Brigade: BG Hugh W. Mercer
(5th, 8th, 32nd, 45th 15th Mississippi Sharpshooters) Wood's Independent Brigade: BG Sterling A.M. Wood
(62nd and 64th North Carolina, 54th, 63rd and 64th Virginia) Preston's Independent Brigade: BG William Preston