linear phase and generalised linear phase filters I know that for linear phase filters, all frequency components have equal delay times. That is, there is no distortion of signal due to the time delay of frequencies relative to one another. 

However, for filters generalised linear phase, where the phase is of the form $a\omega+b$, and $b$ is not zero. Will the same be true for them? Thanks in advance!
Yes. The time delay of real-coefficient linear-phase N-point FIR filter is (N-1)/2 samples. The time delay of complex-coefficient generalized-linear-phase N-point FIR filter is also (N-1)/2 samples.

You can prove this to yourself.  Design a narrowband linear-phase lowpass FIR filter, and plot its group delay. Then multiply that filter's coefficients by a complex exponential whose frequency is one fourth the sample rate, creating a complex-coefficient filter. Now plot the group delay of the complex filter. Compare the two group delay plots.