Do DCT results contain phase spectrum?
Not really, as the transform is real. However, one could interpret the sign as a poor man's phase, being "quantized" or restricted to values $0$ or $\pi$. In other words, $1 = 1.e^{0.\imath}$ and $-1 = 1.e^{\pi.\imath}$. 

[EDIT] There are some instances where people use the sign of DCT or (real) wavelet coefficients, for subpixel image registration or matching, as alluded to in DCT Sign Only Correlation and Its Application to Image Registration:


  In the DCT case, all DCT coefficients are real values, as a result,
  the phase information corresponds to the sign of DCT coefficients.