Yes, as long as it wasn't a felony, violent, financial, or serious crime against ones human rights

However, I will say that some people who may have had an anger issue and made bad decisions in their youth, may have turned their lives around and have meaningful knowledge to contribute to the public dialogue. (And some are just narcissist, sociopaths, out to exploit others). Sadly, you don't have to be a registered criminal to be a bad person with self interests. It's up to the constituent to determine the ideology and character of their representatives.