Is it standard policy to do background checks on every visa application?

To be honest, we are not very sure that the Chinese embassy do the background checks on every application. If you just go for a trip, then the embassy won't ask you to provide the non-criminal record. However, if you apply for Z, Q1, X1 and S1 types, you might be required to provide the non-criminal record. I don't know if you can apply for the non-criminal record successfully.

What's more, you'd better consult with a local lawyer whether you can exit your country when you are on probation. According to what I know, Chines people who are on probation can't exit without approval.