While rice was one of the major crops of the Confederacy prior to the war, so I can understand where your question is coming from, a significant issue with reliance on it for sustenance was the location of where most rice production occurred. Grown in the coastal regions of South Carolina and Georgia, many of the enslavers whose plantations made up the southern 'Rice Kingdom' felt fairly insecure there. Federal occupation of several parts of the coast was worrying to some in of itself, and for most, if nothing else, the close proximity of the forces of liberation was seen as a significant threat towards the enslaved population, in that it might encourage them to make a break for freedom, knowing it was so close at hand. The Confederate 'government' too was fearful of the prospect of harvested rice crops falling into the hands of the enemy and providing them a free food bonus.

The result was two fold. The first was that although there were only very limited incursions in the early years, the US Army did capture rice growing plantations on the Sea Islands, depriving the Confederacy of some production, and also some 10,000 enslaved persons who had labored away on them, by the end of 1861 alone (out of about 48,000 enslaved persons on low country plantations in 1860). The second was that even many of those who were not overtaken early in the war essentially abandoned their plantations as a precautionary measure, moving their human property inland. Those closest to the frontlines were in fact ordered to do so by the army, but others did so voluntarily.

Although those on rivers which mouths were well defended, such as in the case of Charleston or Savannah, were reasonably secure and continued production as normal, the necessity for rice plantations to be accessible by water meant there were easy waterways for raids, or escapes, depending on the direction, or both at once. US navy gunboats would sortie up the river, and regularly return with enslaved persons who asked to be taken away, sometimes numbering in the 100s such as the 24 June, 1862 expedition up the Santee River. By 1863, some more minor rivers had batteries in place to help deter such activities, which did help some planters resume growing and return their enslaved workers, but this only was a matter of reclaiming some production, not expanding it. Further inland, their enslaved workers would be put to work on other agricultural work or leased out for military work.

Again, this isn't to say that rice production ceased, but it was a notable crimp on production, and especially the ability to scale production. In the region itself, rice remained readily available until near the end of the war, and often easier to get then corn or wheat. Recipes that circulated at the time in South Carolina suggested ways to substitute or spread out wheat flour with rice, such as in what came to be known as "Secession Bread",^1 but this was very much local substitutions, other regions of the south had their own different ones based on availabilities. The low country being able to support itself on rice was not the same as being able to flood the Confederacy as a whole with it. When Sherman captured Savannah, his men included in their prize 500,000 bushels of rice (22,500,000 lbs of rice if my math is correct), but nevertheless, the abandonment of plantations en masse, can't be ignored in its impact in terms of expansion

Attempts at jumpstarting rice production elsewhere was attempted in Louisiana early in the war by sugar planters in recognition of the need to improve the availability of foodstuffs (and dropping profits in sugar), but this was fairly haphazard, and of course the fall of New Orleans and American success in the area was a deathblow to the experiment. In a more general sense, while the Confederacy tried to encourage a shift to increased food production from cash crops, passing laws which provided both carrots and sticks, it was often unsuccessful, although in no small part due to their own dissonance, as cotton remained a key crop for financing the conflict, and the government continued to buy it.

So the sum of it is that while the increased substitution of rice during the war was a reality specifically within the rice growing low country, rice production existed in a precarious position for the entirety of the war, which had a significant impact on the industry as a whole, and helped to ensure that rice production wouldn't be able to scale up appreciably so as to become the core cereal crop of the Confederacy. While production numbers in for the 1861-1865 period can be hard to nail down, although hardly the only factor the long term impact of how much land was left fallow is quite illustrative, as the period spelled the death knell for rice production in the region. South Carolina went from ~119m lbs in 1860 to ~32m lbs in 1870, and never really recovered.

Sources

Burroughs, Frances M. "The Confederate Receipt Book: A Study of Food Substitution in the American Civil War." The South Carolina Historical Magazine 93, no. 1 (1992): 31-50.

Dusinberre, William. Them Dark Days: Slavery in the American Rice Swamps. University of Georgia Press, 1995.

Hurt, R. Douglas. Agriculture and the Confederacy: Policy, Productivity, and Power in the Civil War South. University of North Carolina Press, 2015.

Thomas, Emory M.. The Confederate Nation: 1861-1865. HarperCollins, 1979.

Tuten, James H.. Lowcountry Time and Tide: The Fall of the South Carolina Rice Kingdom. University of South Carolina Press, 2012.

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1: If you want to make it: 1 gill of rice boiled very soft, when cold mix in 3/4 lb of wheat, 1 teacup of yeast, 1 teacup of milk, salt to taste ? mix and let it stand 3 hour, then it must be kneaded in flour enough to render the outside hard enough for the oven. In an hour & a quarter after bake it.