Is there a biological link between anxiety and Crohns?

You might be able to link Crohn's symptoms to anxiety, but even very high anxiety levels couldn't manifest the disease itself. No different than someone experiencing a lot of stress, will sometimes get an upset stomach and diarrhea, or several other nervous system responses.

Statistically speaking, people with IBD have higher rates of depression and/or anxiety than the general population.

I heard a researcher say that it's not surprising for two reasons: One, the psychological stress of having a chronic illness, plus the issues of needing the bathroom urgently. Two, they have evidence that the pro-inflammatory cytokines active in IBD can and do cross the blood-brain barrier and likely have biological impact on the brain.

So the answer is, yes, Crohn's can cause anxiety, both psychologically and biologically, although the latter isn't well understood.