I work hundreds of these every single day and I know the expense. To ensure good speedy, bar-coded delivery use good stock and leave white or light space on the front lower right for the bar code. No dark handwriting there either! Post cards should have all the bottom clear enough. The code can get masked by dark background. Barcode ink may smear on some shiny surfaces(even pro mailers can make less than ideal mailings). There is a light red code put on the lower back which also might get blocked so leave space there too although that should not slow anything down except the machine stops now and then with too many red code failures. Mail as early as is practical. Ask the office for advice. Barcodes keeps mail automated and fast. Otherwise it gets kicked to manual sorting.
MOST will get through and on time, no fear, but optimize! To see how things go you could include some return address, preferably some neutral box or headquarters. All first class mail should get return service and forwarding. The yellow stickers we put on for address corrections or return are kinda awkward on postcards but they mostly work real well, except those pass alongs can get very slow.
Research all practical ways that can help a campaign.