I am going to point out that I do not approve the additional layer of drywall for ceiling. I just answered a question here - Should I use 1/4" drywall to cover ceiling texture or imperfections? - that addresses my concerns with an extra layer of drywall on ceilings.
I love doubleing up drywalls on wall (vs furring out) so I am definitely "liberal" on using drywall. I just don't like the extra weight and have had to go back and repair in the past. Add on a basement - the movement above - has to make it worse. I understand the doubling for noise but is that providing a better solution than stuff the joists with mineral wool? Also with a double drywalled ceiling... lights, fans, boxes become more complex.
Now I will just answer your question. No you don't need a normal screwing pattern. 16 screws per 8' is enough - but the key is to glue to the joists. I would also double screw the bottom layer in. This is a technique where you use the same screwing schedule and set screws about 1.5-2" apart for each pop. So everywhere you would put one... put two. It is a given that you will need longer screws to match depth of the drywall above and yes I would glue this too.
But to answer your question there isn't a rule for a set schedule in this place because it is still screwed in by the other screws.
I have done a lot of sound proofing work. I never saw a company that offered to double drywall. I am not saying it doesn't help - but between "sound proofing" guys, green companies, drywall crews, and general contractors I have worked with I think one of them would have brought this up (I have done A LOT of basements) if it was something that was worth it. The fact is you are making your install harder and making future issues harder to fix/troubleshoot. Seems the focus should be packing the cavity.