If someone registers this week for CS executive New syllabus Dec 23, will he be eligible to give both groups in Dec 23?

This depends on your choice. Yes, you can do both.

But it needs huge prepartion to pass both at the same time.

The december session of CS Executive will be held from December 21 to December 30,2023.

There is only few months left, Prepare hard and give your best as best as you can.