It very well may, but it is possible it will not. It really depends on the nature of the background check, how deep the check will go, and how closely the checkers will look at what may be some red flags of non-citizenship.
Good luck to you.
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The 1986 Immigration Reform and Control Act (IRCA) requires that employers verify that all employees have proper work authorization. Employers must complete Form I-9 within three days of the start of work for each employee. I-9 info is then checked by E-Verify, a computer program used by the Department of Homeland Security ("DHS") and the Social Security Administration. E-verify confirms the employee's authorization to work. Unfavorable determinations and claims of error can be appealed.
DHS enforces laws against unauthorized employment, along with the Immigration and Customs Enforcement Agency ("ICE"). Employers are audited for compliance with all legal requirements.
There are civil and criminal penalties for employer violations of these laws. The penalties are potentially very severe, and can put the typical employer out of business. For example: violations of records and documentation errors subject the employer to penalties of $110 to $1,100 per each insufficient I-9; employment of unauthorized employees can cause penalties of $3,200 - $16,000 per unauthorized employee. Criminal penalties may include up to six months in jail and/or a fine of up to $3,000 per unauthorized employee; and
imprisonment of 5 years for 10+ unauthorized employees in a twelve-month period (with actual knowledge).
Enforcement of these laws steps up each and every year, and you must realistically expect that at some point your employer will necessarily be required to verify your employment status and will be required to undertake such verification measures as will reveal the problem with your status. You need to get in touch with an immigration attorney to do what can be done to resolve your work eligibility. A consultation with an employment attorney would also be a sound step for you to take. Your employer may be antagonized by the jeopardy your deception has created and there may well be push-back.
These are knotty facts and there are high-stakes for errors and omissions. You need legal skilled and experienced legal counsel for all of the issues raised by your situation.
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I own a company that performs background checks. Typically, the checks do not reveal whether or not a person is authorized to work in the USA. The check will verify criminal history.