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If I have already played Birth ME code, will any of the plot points in this game be spoiled? I know they are in the same universe, but is one designed to be a prequel/sequel to the other?

Both games technically spoil each other, and also technically don't spoil each other. I would say Birth ME Code to Head AS Code is simply a different experience than Head AS Code to Birth ME Code. Different things will be suspicious, different characters may be interesting, and some twists from BMEC will be more relevant if you played HASC while other twists from HASC will be more relevant if you played BMEC.