Don't quote me, but I don't think that should be a problem. You're not hired by a US employer so their laws don't apply. If you are in an interview and they ask, be honest about it. You need to eat while you wait for them to take years to adjudicate a case. From what I've heard from a friend, they won't penalize you for that, and she was working 'under the table' here

I am struggling to get a Job, I haven't received an EAD can you refer the company you work for please.

yes they count it as job,talk to lawyer