Current state

Alpha

The game is currently in Alpha state according to the developer. Sign-up for joining alpha-testing is available through the official Pax Dei website and may involve an NDA.

The first wave of Alpha testers will be invited "before too long™" and will start in a region of Gallia.
Here is a quote from the developer which gives a more detailed answer to the current state of the game:

We are coming up to a stage where we think we can offer a large number of Alpha testers an enjoyable stay in a relatively stable client, with enough to do to start feeling at home in the world of Pax Dei. But obviously there are a lot of things yet to be implemented and a huge amount of content that needs to be produced for a full and proper launch.

We have been doing smaller play tests for a long time now, only by invite and under NDA and we will be expanding on that in the coming weeks and months. I cannot say right now when we let people in by the thousands, I would not be doing anyone a favour, but we want people into the alpha client as soon as we can be relatively sure they are not going to be frustrated by server and/or game performance.

...

Some further clarification was added recently, here's another quote:

We’re still a few months away from a large-scale Alpha test. Rest assured that when we’re ready to announce it, we’ll publish official communication with all details.