The simple answer is yes, they can.
It is a very complicated process. The process must be started well before a Chinese national holding a Mainland passport even comes to Thailand, unlike many nationalities.
It requires them to get a certified marital status document from the Chinese government in China. Then to have that document translated and certified in China. Then again by the Thai Embassy or Thai consulate there in China. You must have the documents fully certified before coming to Thailand. This is required in order to legally register your marriage under Thai law. There is no way around this.
Chinese nationals are allowed to marry most any foreigner, not only a Chinese national, legally. So Chinese legal marriages can be registered under Thai law in only a few places in Thailand. Most registrars will do it.
If you wish to arrange your legal marriage in Thailand, please contact us through our contact page and is best to use our questionnaire for the service, as we need many details, to answer correctly.
This post is not meant to be a full detailed explanation of the process. Because this is not meant to be a DYI explanation of the entire process. As the process and requirements change depending on the nationalities involved. In fact, I do not recommend that any Chinese national try to do it on their own.
If you contact us, I can explain the procedure as it applies to you as a couple.