Ultimately, none of us can answer this question, because the motivations for doing background checks vary widely among employers. As a result of that variation, interpretation of the results also varies widely. Some employers will care about things that others don't even look at.
That said, it's somewhat common for candidates to leave jobs off their resume for various reasons. Some people with really long resumes will prune jobs just to keep the resume at a reasonable size. Other times, when a job isn't relevant to the specific opportunity at hand, you can leave it off for that reason. Most employers understand that, and many will be totally okay with a job being left off.
Employers don't like being lied to, but leaving a job off your resume doesn't automatically count as a "lie" in every case. Some employers will want to know about every position you've ever held, but the good news is that those employers will make their needs known - they will tell you to list every single job at some point in the hiring process. If you weren't explicitly asked to give details on every single job you've ever held, leaving a job off your resume is likely not an issue.