Intuitively, yes.

If something is irreversible then it's not 1 to 1 and you don't use the whole state space, so you'll likely have short cycles.

Second part, again yes. But you can add that useful irreversible transform in the finalization of the output, and not in the state transform itself.

I'm self taught so my understanding and terminology may not mesh with the people who have been taught this.

CSRNGs are mentioned a few times in TFA, but cryptographic security doesn't appear to be among the design criteria for SHISHUA. There's no mention of linear or differential crpytanalisis, which is table stakes for a CSPRNG.

I added a warning in the GitHub’s Readme. SHISHUA is not to be used for cryptographic purposes.

You mentioned the lack of cryptanalysis; there is also the lack of rounds (which prevents researchers from breaking partial versions to ease their study, and allows setting a security margin).