Depends on the game. Some are patched for no CD (Like 1776, Squad Battles, etc etc) but others have not been patched up yet to include that. So for now yes depending on what title you choose. Check the patch notes to see
If you are worried about your original game disks getting scratched and damaged from repeated use you can copy the .exe files from each HPS game and write them to a blank disk. Then that way you can play all your games from just the one disk. It helps to save wear & tear on your originals.
At the moment only Chickamauga, Corinth, Gettysburg, Ozark & Peninsula are playable without a disk.