There were shortages even before the war and:
"The invasion in June 1941 thus disturbed an already delicate balance of food supply. This was made all the more serious both by the very rapid advances of enemy troops into what had been amongst the most productive of Soviet agricultural areas and by the eastward movement of refugees. Some 10 million souls were evacuated to the east, thus increasing demand in the residual agricultural areas."
"Rationing was the obvious and immediate response to such pressures,...Food rations were differentiated according to status from the beginning. Rations for the armed forces were highest and dealt with quite separately. Initially there were four categories of civilians for ration purposes: manual workers, clerical workers, dependants, children up to 12 years inclusive.19 In addition,manual and clerical workers in high priority industries (war industries, chemicals, fuels, metals, transport) received a higher bread ration."
Note that the army got more food, but still it was rationed.
And the food supplies from the USA, that Sardaukar commented. Important to note that the peak is when in the game the initiative switches to the soviet side, and still they needed a lot of food imported!
. So probably it depends. 
