If it's anything to do with the government or similar then it may have an impact. I know places where temps are not subject to checks but official employees are so a temp who is taken on by the place could have been working for months unchecked then have to be checked to be cleared for a permanent position.
Some places can have very strict policies nowadays, I know of ones where all staff, however junior, have to be credit checked and no clear check = no job.
If I was an employer where something came up an employee hadn't been honest about I'd be wondering what else I might not have been told and question their integrity. They may just be looking to protect themselves from more serious "criminals" and may be fine if she is honest and explains.
It could also impact on reference and getting another position should the worse happen and she end up out of a job because of not coming clean.