Does the Chinese consulate carry out criminal record checks or should he not worry about it?

Jessie, I don't know whether they are able to check your criminal record. But I do know that some people who even committed crime got the visas to visit PRC. Many people might have a doubt when filling the application form because there is a question "Do you have any criminal record in China or any other country?". They don't know whether they shoul check Yes or No.

According to what I know, people who checked Yes finally got their entry permits. But I personally think that it's good to check No even you have criminal record. In this way, you have bigger chance of being approved. My advice for your reference only.