Can I powerwash a paver-stone patio?

Tes you can, I have power-washed mine several times

It doesnt look like anything is holding them together though?

Sure, you can power-wash it. I don’t know that it’lll kill the moss, but it’ll get rid of it, at least for a while.

How far apart are the stones?

They are very close together. It is in a house that I am closing on May 6th. It almost looks brick, but they are different shapes.

Power wash will work.
There are also products you can purchase to assist in the kill.
Here is a link for a DIY approach

I have used products to control it in my yard in the past and they work pretty well.

I wouldn’t worry about whether the stones are “held together”. They’ve likely been there for a while and are probably pretty solidly laid.

We used to power wash our pavers in FL. They were not held together by anything except at the edges they were “cemented” down. There was sand in between the pavers, and sometimes some of that is lost when you power wash them, but I would not worry about that. The guys who do it for a living sometimes use a chemical, not sure if it is bleach or some derivitive of to get them really really clean. But, just water should help significantly.

After the wash you might have to add some additional sand to the joints.. Easy fix.
This might help…
Pressure Cleaning and Sealing Pavers Re Sanding and color sealing for pavers
http://www.floridapavers.us/clean_seal.htm