Things work differently in different parts of China, and change constantly.
I believe this is the current situation.
Some provinces (for example Jiangsu) demand a Police check, but I'm not sure all do. I think all of them will at some point give you a form (probably the health check) with a checkbox about whether you have any criminal convictions, and if that's the extent of their checking up on you, you could and maybe should tick no.
I'd suggest asking employers fairly early on what documentation you will need if you accept a job, which should give you an idea of whether this will be a problem. Of course its possible that the need for a thorough criminal check is now being implemented in all provinces.
I think even where they do a criminal check, they may not care about a DUI misdemeanor. if there is a solid rule in this regard, I've not heard of it. As you're unlikely to be driving in the country, I'd have thought that this would be very low on any list of concerns, but I dare say that some provinces and Police offices do turn people down for any criminal convictions. You wouldn't get that many people coming on to forums like this and sharing the details of why they've been turned down. It's all folk such as yourself asking whether they would be.
I'm afraid you probably won't get any definitive answers for the whole of China. The best you can hope for is a definitive answer for a province or city. i mean, if you were applying to my province i could ask my FAO for the current situation. Things could well change though between now and the point when you apply for jobs (which will need to be about the end of April, though there will be jobs available later than this of course).
They're mostly concerned about sex and drug offences, and over the last few years the need for criminal checks was introduced earlier for those working with children.