No, no, and no. There is so much BS and misuse of statute going around on this issue, that I'm surprised this hasn't become a major issue in the military justice system. There are several issues to this thread thus far which I will attempt to deal with independently.
1. To the original poster: I'm assuming your case (or hypothetical) is aimed at a perp who is observed drinking or being drunk, then subsequently driving, but not stopped by competent legal authority. Now, such a person could be brought before his CO for NJP, as normal rules of evidence do not apply, but a wise perp would push for a court martial because there was (I'm assuming here) no evidence of actual impairment. I'm also assuming that there were no witnesses that could assert beyond reasonable doubt that they, as laypersons could have assessed the perp to be under the influence to the extent that said perp was unquestionably impaired. I know we're not operating on all the details or facts here, but bottom line vanilla version is that having a bystander witness someone drink, then drive should not be enough to convict then in a court martial for 112, or 134.
2. Double Jeopardy: A perp can not be held liable for the same charge in multiple jurisdictions, nor can you attempt to fling a tangential charge like 134 at him to cover an offense which has been disposed of by military or civil authorities. This has historically been one of the most abused areas of the UCMJ, where a perp will get charged with DUI by local/state jurisdiction, then charged again under the UCMJ through 112 or 134. To do so is double jeopardy, and there is ample case law to support a defendant if they push for a court martial.
3. 134 vs. other articles: You can not charge a perp under multiple articles for a single offense, or even use 134 as a catch-all if the others don't happen to stick. Again, most of the abuse in the system comes from NJP proceedings where an ignorant/overzealous CO presses for what amounts to double jeopardy, or where the evidence would never meet the burden of proof in a court martial.
Bottom line: Any serious offense (including DUI) requires retention of counsel to determine whether the facts warrant disposition at NJP or court martial, as the potential for abuse or ignorance at NJP by the COC is especially strong.
Brett