Checksum has nothing to do with handshake. It simply validates integrity of a packet being transmitted. If packet is invalid, it will be discarded. In case of TCP, receiver (or rather a next hop router) will try to recover by asking sender to re-send invalid packet. But in case of UDP, it simply ends right there - packet is simply discarded and that's it. Beware though that UDP checksum is actually optional. And I believe can even be removed by an intermediate hop router. It's also a pretty weak checksum even if used.
In general, modern day "common wisdom" says that on modern equipment packets rarely get corrupted in transmission. And if you're ok with that assumption, then I'd suggest simply assume that packets are never corrupted ignoring whether checksum was used in transition or not. But if you aren't ok with occasional data corruption, then you should rather embed a better checksum into your data, such as a CRC or even a cryptographic hash. It all depends on how important data integrity is for you and how far you are willing to go to achieve it. And that actually applies to TCP as well as to UDP.
See RFC and also this answer.