Yes, Apple can and does design chips. But as you can imagine - "Designing chips" can mean anything.

With respect to CMOS chips you can go from from calling up Sony and ordering one off the menu with your custom requirements, to designing the NAND/pixel interconnects, microlenses, downstream dual-gain architectures, to working on the bonding chemistry, masked pixels, CFAs etc, etc. However, all this stuff is patented up the wazoo, and companies like Sony, Samsung, Aptina, OmniVision etc do not simply hand-over world-class tech like this.

Apple is very good at supply chain logistics, overall packaging and design, UX, Software, etc. However, I don't see them challenging the established players on core technology.