It depends. In some cases, they do not, but the legislature may have closed this "loophole", so by the time you read this the law may have changed. The Missouri state supreme court had decided earlier this year that they did not count under the existing law, so the legislature is likely to change the law. The Missouri Supreme Court ruled that these convictions are ineligible as prior offenses for perfectly legitimate legal reasons - in these cases, the defendants were not given legal counsel, and never waived their right to counsel.