Yes it is possible.
This could be hardware and driver dependent, and might be very different depending on what other types of packets are being sent over the line at the same time.
How are internal packet buffer is handling the incoming send requests? You can't know. It could be using parallel buffers that fill up in odd ways. Since the spec doesn't have a guarantee, there would be no reason for the implementer to bother keeping things in sync (esp. considering the speed gains with lack of overhead).
A windows box might decide to send a NTP time update request and a network share scan, and then while in the middle of that, dropbox could make a request for local folders. Now any data in buffers are suspect.
You could send millions of packets and not experience this issue. But it is a possibility. The chances of it happen may be small, but it will happen.
The only real way to guarantee that these aren't going to cause problems is if you are running your own OS and have explicit knowledge on how the hardware performs and have the driver source code and the UDP api's source code.