Is the phase difference between recorded sounds from left and right ear the same as the phase difference between their HRTF?
Consider a signal with a particular frequency at phase $\alpha$. Passing this through the two filter paths changes the phase of the frequency to $\alpha + L$ and $\alpha + R,$ where $L$ and $R$ are the values of the phase frequency responses of the two HRTF filters at the particular frequency. Yes, the phase difference $(\alpha + R) - (\alpha + L)$ is equal to $R - L,$ which you call more simply the "phase difference" between the HRTF's.