IANAL, but definitely you can use acronyms as trademarks. As you pointed out, IBM is one famous example.
I imagine it'll be an issue if you actively used "Carrying Cases for IBM Computers" as, say, your tagline. But using CCIC as your mark won't necessarily be, assuming others aren't using the same for a similar or competing business as yours.
In short, if you market your product or service as merely CCIC, barring above, you should be good to go. Should be, anyway.