Sodium permanganate from manganese dioxide and sodium hypochlorite
I performed this reaction, and the answer is yes, concentrated sodium carbonate can be used in place of sodium hydroxide, though the latter works better. The reaction goes under normal pressure, but it requires heating. The rate of the reaction also depends on the quality of manganese dioxide - freshly prepared works best. You will notice the formation of permanganate as soon as you boil the reaction mixture, but complete conversion of dioxide may take several minutes to hours. If you want a complete conversion, better use the sodium hydroxide.