*please help* Will my previous work history count w no paper trails?

Hello my fellow nurses!

Hypothetically, let's say someone worked at a clinic when they did not have legal work authorization (no ssn or itin on file). And now they are at place where they can legally work. When they apply for new inpatient jobs, no work history/tax reports will pop up under their name/ssn. Now, will their work history count if it is on resume+ reference letters while it does not pop up on their background check? Will it be safe to openly admit that they have work experience as a nurse wo work authorization during the hiring process? 

If anyone can also list some immigrant nurse communities or people familiar with healthcare and immigration, that would be amazing.