Extremely unlikely. but maybe. But it would not be a Sun if no fusion occured. What is the maximum possible melting point at a million times a million times a million, times a million, times a million = 10^30 times sealevel air pressure?
Possibly, If we could assemble the mass of our Sun in a sphere about that size, without getting it extremely hot, fusion would not occur and the core would be solid. If the assembling took place very slowly = billions of years, the heat of compression might be radiated away, so that fussion did not start even though the core pressure was huge. Possibly a white dwarf or neutron star would occur without there being any fusion. By definition it is not a star without fusion. Brown dwarf stars are not considered stars for this reason, and some brown dwarf stars are cool enough to have solid cores. All brown dwarfs are thought to have less than 8% of the mass of our Sun, but possibly there are very rare brown dwarf stars with more mass and no fusion. Neil