Yes it is very well possible to get an event Pokemon with a different Nature.
You are only required to do the following
- Receive your Mystery Gift
- Save your game before talking to the Deliveryman
- Keep coming back to him or softreset until he gives you the Nature that you desired for the Pokemon
I have done this multiple times, including with the Deoxys event and it has always worked for me :)
P.S: The Nature of the Pokemon wielding Synchronize will not be passed down to the event Pokemon (as for now)