The hot chocolate mix will produce a less chocolatey cheesecake and contribute a distinct brown-butter-like flavor you can't get from cocoa powder alone due to the milk solids.
The more hot cocoa mix you add, the more of its flavor you'll be able to taste, but be cautious about adding too much since you don't want the cheesecake to come out dry.
For a standard recipe with three to four blocks of cream cheese, stick to ⅔ cup or two packets of hot cocoa mix. If you add more, make sure the batter remains pourable and creamy.