During the application and interview process, was there any question asked to which an honest and literal answer to the question would have revealed the felony?
Example: Have you within the last seven years been convicted of... honest answer - no.
Have you ever been convicted of...honest answer - yes.
You are not required to volunteer the information. If you were not asked any questions, either on paper or in person, where answering honestly and literally would have revealed it, then you technically have not withheld anything. Can't carve anything in stone, of course, but that puts you in a much better position than the alternative.
If there was something asked and you failed to disclose it, then when it shows up in the background check it's likely that you'll be kissing the job goodbye.

