I did a change in a metadata of a class (ClassName.cls-meta.xml) If I would deploy ClassName.cls apex class through change sets, then file ClassName.cls-meta.xml would be deployed also?
Yes, as long as you have push your changes to the source org, whenever you create a new change set, the configuration file will be included. for example, that's one way you deactivate triggers in a production org. you edit the
trigger-meta.xml file, as explained here