To answer your first question, does the data get discarded? Yes it does. The IP & ARP protocols come into play when your packet is larger than the Path MTU. The Path MTU is the maximum transmission unit of the path between your client and server. Assuming that your NIC card is a standard ethernet card, then your maximum MTU is 1500. Now, lets assume that the whole Path MTU between your client and server is 1500. In this scenario, if you send any packet that is greater than 1472 bytes (1500 - (20 byte ip header) - (8 byte UDP header)) then IP fragmentation will occur. What will then happen is that the IP layer will chop the packet into fragments to meet the MTU of the ethernet link. Now, before any data can be sent, the MAC address of the destination needs to be resolved. So all of a sudden, the ARP protocol will receive multiple IP fragments requesting the same IP to MAC address resolution. What will then happen is that ARP will initiate an ARP request for the first received packet and wait for the ARP response. While waiting, ARP will discard all of the fragments making the same ARP request and queue only the latest arrived fragment. Therefore, if you send a packet greater than 1472 bytes, don't expect to receive the whole packet on the other end if your ARP cache is empty.
Does the newly arrived packet get appended to No, it doesn't get appended. UDP is a datagram protocol with strict message boundaries. Therefore, each arriving packet is considered as a complete self-contained datagram; the data will not get appended.