I don't know if colonoscopies are covered by Medicaid; I've never had one yet. (Yeah, I know, it would be a good thing to check just in case.)
I have done one of those mail in fecal/stool sample tests for my private doctor. It was covered; however, I was under my ex-job's benefit program. I was paying $700 a month for such coverage. Yikes.
They didn't do a colonoscopy on me; but an MRI on my lower chest.