I believe you need to consult an attorney in South Carolina who is familiar with the sealing and/or expungment statute in that state. In Florida, the court ordered expunction of a criminal record is controlled by section 943.0585. Part 4 of that statute explains the effect of a criminal history record expunction - or benefit as follows: "the person [who's record is expunged] may lawfully deny or fail to acknowledge the arrests covered by the expunged record, except when the subject of the record: 6. Is seeking to be employed or licensed by the Department of Education [or] any district school board."
So if your arrest and PTI charge had been expunged under Florida law you would still have to disclose it in your application to any school board. That is why I believe you need to consult with an attorney in South Carolina or at a minimum read the South Carolina statute that authorized the court to expunge your record. Your answer will likely be found there.
You also need to be aware that even if you are "legally" entitled to deny the existence of the charge in South Carolina it still might not be in your best interest to do so if, for instance, the school board might find out about it anyway. Private companies often mine public records and create their own data bases which they then sell on the internet. If one of these companies got a copy of your arrest prior to the expungement then a record of your arrest might still be available to the public. Try to do a background check on yourself on line to see if you can still find the record. If you find it, then it might be in your best interest to include it in your application and then explain it in your own words. I don't think that it is uncommon for people to have minor run ins with the law in their past as long as they are isolated incidents. Try to make a negative a positive - tell them how you learned from the mistake. Good luck.
This answer is not specific legal advice, nor does it establish an attorney client relationship. Generally yes, if not the failure to disclose can be a basis for denial, even if the charge itself is not.