To pursue PHD you need to have your post graduation done. PGDM is a diploma and not degree. In case a college offering PGDM degree has AIU approval, it would mean that the PGDM offered by the college is equivalent to MBA and will be recognised as a post graduate degree. So for PHD yes it would matter if the college is not AIU approved.
But incase you are pursuing a PGDM which is not AIU approved, you can consider going for a FPM degree instead of PHD, FPM is similar to PHD and is equally recognised. Incase you don't wish to go for FPM, you will have to invest one extra year in pursuing an executive MBA and thereafter you can go for you PHD.
Lastly, in case of government jobs, not all government jobs require you to hold a post graduate degree.