when apply for GC

If you will go back to China after your H1 6 years, really no one care. But if you want to file for GC or change status after your future H1 ends, it is you that need to provide proof of legal status and work authorization during all these year including this status gap, not the USCIS officer's burden. If you want to be eligible to file I-485, you need to provide these proof. Or you are not eligible to file within USA.