I was under the impression that everyone would be using the same centralized server being operated and maintained by the Mercury team themselves, just as you do when you use a centralized exchange or a mixer.
That's my understanding too. It seems to be open source so you can technically download Alice's version and use Alice's server, or even configure the "original" wallet to connect to a different SE, but that's no different from using scammychipmixerclone.com.
https://github.com/layer2tech/mercury-wallet