No, they won't show because of the method used to obtain a DEPT spectrum.
13C spectra, if they were taken in the same manner 1H spectra were taken, would show enormous couplings between the carbon and any protons on it. This would make spectra difficult to read. Instead, the proton range is irradiated to decouple the protons from the carbons, collapsing the expected multiplets back into singlets. Very strong singlets due to the polarization transfer, which is why even in a normal 13C spectra, the quaternary carbons have very weak signals compared to protonated ones.
In a DEPT spectra, the irradiation is tuned to give a specific tip angles for the protons, and the spectra collected in the carbon range. Only the carbons which have protons and can exhibit polarization transfer will show, and different tip angles will cause different arrangements to show.