I don't think so.
What you said may be true. But the key is, whether this would cause a problem in job seeking, it depends on how employer think.
I don't think most employers here know the big differences between national company and the international company in China, never metion whether they would be much concerned about it.
I think the technical skill is the most important, and this seems is LZ’s strong point. English is as the same importance for sure.