You generally shouldn't need to check for this, as corruption is extremely unlikely if the transfer is successful.
From Wikipedia:
AirDrop uses TLS encryption over a direct Apple-created peer-to-peer Wi-Fi connection for transferring files.
While TLS is not specifically intended as an error-detection method, it will effectively act as one, because if anything is corrupted in transit the decryption will almost certainly fail.
In addition, WiFi has CRC error detection at the link layer.
The only kind of corruption that might get around these checks are if they happen at one of the endpoints when reading/writing the file, not in transit. That same kind of problem could occur if you're simply copying a file on the same machine, it's not related to AirDrop.