If you completed deferred successfully, and you got your Petition for Non-Disclosure granted and signed by the judge, then all the documentation surrounding this arrest should be SEALED. This is different from an expunction. Where an expunction would legally allow you to deny ever being arrested.
The sealing of your records is targeted at not allowing private agencies to see your record. However, what private agencies depends on who has access to this information. Your lawyer, hopefully, inlcuded publicdata.com in the Order for NonDisclosure, as they are probably the leader in background checks. However, there are many other agencies out there and if one of these agencies got your public criminal record information before you got it sealed, then they still have it in their system. Any private agency should not be able to get your information after the date of sealing. However, it's almost impossible to determine who has your information before the date of sealing. Basically, you'll only know if it comes back during an interview, and then it is too late.
As for the FBI, yes, they have access to your sealed record. As for the finger print, it depends on which database your print is run against. The State should have sealed all these records if the Petition was executed correctly. However, if they run it through an FBI database then you will show up.
Try and run yourself on publicdata.com and see if your record pops up. Otherwise, it is basically up to you whether you disclose it to the school. If you disclose it, you don't get the job, if you don't then you risk them finding it and you don't get the job. It's up to you.
Please feel free to contact me for a more thorough complimentary consultation. I will be able to search your record and see if it is truly sealed.
God Bless America,