Certainly it was not impossible to cross the Mississippi River by avoiding the Union gunboat patrol in a covert manner. And regular communications between the Trans-Mississippi and Richmond, were maintained in this manner after the fall of Vicksburg. In fact the confederates had quite a little system for blockade running on the Mississippi in 1862 and '63.
But in reading Harold Simpson's "Hood's Texas Brigade, Lee's Grenadier Guards" It relates that Lee' asked Senator Wigfall on two different occation, once after Gaines Mill, and the second time after Sharpsburg/Antietum, about the need for more troops from Texas to refill the depleted ranks of that Brigade after those battles. Yet when he did have replacements in his hands by the exchange of the Arkansas and Texas troops from Arkansas Post, exchanged at City Point Virginia, available to him, the Confederate War Department did not take advantage of that situation and instead transferred them to Bragg and the A.O.T. Why?
Did it have something to do with the conditions of their parole and exchange? City Point was not the "normal" exchange point, as I said, for soldiers captured in the Trans-Mississippi. So the exchange was extraordinary it that manner. The troops were the 6th, 10th, 17th, 18th, 24th and 25th Texas, and the 19th and 24th Arkansas. The 17th and 18th were consolidated as were the 24th and 25th Texas and the 19th and 24th Arkansas.
Now, I know that Trans-Mississippi troops were not well thought of in general in the eastern theater early in the war, and that is one of the often stated reason for sending those troops to Bragg. But by mid 1863 the Texas and Arkansas troops of Hood's brigade had well proven their worth in a fight. And that reason seem childish if true. By 1864 and '65 when all practical possibility of transferring any troops from the Trans-Mississippi to the east was well past, Richmond was screaming for these troops and abandoning the west all together. In at least two Brigade histories, I have read (Kershaws Brigade history for one), the writter complains bitterly about the 55,000 troops in the Trans Mississippi who were doing nothing while Lee's army starved around Richmond.
I also realize that co-operation between the various confederate theaters were almost non existance, but that is a different matter and subject.