You'll probably be OK.
Did you discuss this with the company's immigration lawyer yet? If not, do so tomorrow.
And ... don't talk to a non-attorney in HR ... stick with lawyers for legal advice.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
You should let your lawyer know this and follow his advice. Best Wishes!
Attorney: Immigration Law
13295 Illinosi St Ste 128
Carmel IN 46032
Ph: (317) 660-6174
Contact (317) 660-6174 for specific legal advice. Answers here are not legal advice because they are of general nature and not tailored to your specific situation. You should not act on this answer without checking with an Immigration Attorney.