Most likely no. With those tests they are looking for something specific and would not test for the presence of something that does not relate to that.

No, this would not happen.

The myth about the guy who takes in a urine for a drug screen, and they tell him "congratulations, you're pregnant" is just a myth I believe. There would be no reason to test for pregnancy.

I work in a lab, and the only time we test for pregnancy is when it is specifically requested. It would *never* be requested on a diabetes checkup. However, if you were about to have surgery, it may be requested by the doctor. They don't even have to get consent for that, as the foetus' right to not be anaesthetised overrides yours. It may also be requested by the doctors if you come into the emergency department, before they give you any treatment that may harm a foetus, or for diagnostic purposes (abdominal pain, vomiting, etc).