The short answer is YES. But like anything in Digital Forensics, the real answer is...
It depends on the version of CCleaner. It depends on the Operating System and version. It depends on the applications used. It depends on when CCleaner is run. It depends on if backups of your system were made. It depends on if your system utilizes full disk encryption.
Also, note that unless whatever tool you use shreds the information to make it nearly unrecoverable then it will recoverable after some time when it is removed. SSDs actually are better to use for keeping things from being found then normal HDDs.
Sometimes proving that CCleaner or equivalent was run can be just as damning -- reference to the files could still be found in MRU's, Registry (can use tools like Yaru for instance to undelete Registry items if the registry hasn't been compressed), Volume Shadow Copies, etc
@Lids : You bring up an interesting point: the absent of data can be just as damaging as finding the data. Proving someone covered up deletion of data can lead investigators to know something was going on this would be the same as trying to clean up blood from a murder scene.
Agreed @azuleonyx, sometimes proof that a cover-up has attempted to be performed - accompanied by other supporting evidence - will be exactly what's needed ahead of the custodian interview to obtain a confession or steer the conversation in a certain direction