They might. Some facilities will forward mail that arrives with an incorrect address, particularly if the inmate's name and ID number are on the piece and staff can match it to a current resident or a recent transfer. But forwarding is not guaranteed, and it is entirely up to the receiving facility whether they make that effort.
Do not leave it to chance. If you sent those postcards through InmateAid, email aid@inmateaid.com with the correct facility information and InmateAid will resend everything to the right address at no charge. That is the fastest and most reliable way to make sure your inmate actually gets what you sent.
Piedmont Correctional Institution in Salisbury and a Raleigh address are far enough apart that forwarding is unlikely without the right inmate details on the piece. Getting the corrected address into InmateAid's system now means the resent postcards go out promptly and arrive through normal mail delivery rather than depending on an overworked mailroom to sort out the error.
Going forward, always confirm the full facility name, city, and zip code before placing an order. InmateAid's facility database is regularly updated, so searching by facility name directly on the site is the most reliable way to make sure the address is current before anything goes out.