If you are really trying to do a Williamson ether reaction, I suspect that you would want to add the base and the phenol together first to form the phenoxide (usually turns a dark color in an aprotic solvent). The equilibrium concentration of the phenol varies depending on whether sodium carbonate or sodium hydroxide is used (differing pKa's). The second reaction will be the same since the reacting nuclephile is the phenoxide. If you form alkenes, the phenoxide is capable of an E2 reaction (picking off a proton with halide elimination), although the alcohol would seem to be formed only from the hydroxide. I don't suspect that you would form appreciable amounts of organic carbonates even if you added the components together, although I could be wrong.