Such recipes will appear in the crafting menu and can still be crafted as normal, but they respond to CCOR's filters and toggles. Recipes added by other mods will not automatically work with CCOR's menu options.
Please check there before requesting patches. Refer to Patches Under Construction to see which patches are currently being worked on. Patches and links to patches can be found at Kryptopyr's Patch Hub. The script changes will either need to be combined, or you will need to allow CCOR to overwrite the scripts. Mods that edit the MineOreScript or the ResourceFurnitureScript will NOT be compatible with CCOR. In order to preserve CCOR's consistency, you will want to load CCOR after such mods, or create a patch to merge and carry forward the changes from both mods. Mods that make changes to the vanilla crafting recipes will likely conflict with CCOR. The primary reason for patches or built-in support is to provide consistency and allow other mods to take advantage of CCOR's crafting filters. This means that you can safely use most mods alongside CCOR without needing patches. Note that without built-in support or patching, items added by other mods won't benefit from the menu filters added by CCOR, but neither are they likely to create any serious conflicts.
Mods that add new armors, weapons, or other items to Skyrim should work just fine with Complete Crafting Overhaul Remastered.