BI Service Update

I'm preparing for go live and I'm wondering how people manage to regression test the BI service updates. 

You can't

Is there any way to know in advance when a BI service update is imminent or when one has just happened?  

 No

Is there any way I can pause updates so that we receive them at weekend?

No

Is there any kind of version number that I can track?

Yes, In the Service, you can click on the "?" in the upper right of the header. Then select "About Power BI" and the version is one of the metrics that will be displayed in the popup.

Am I worrying unnecessarily - do things rarely break?

What are you worrying about breaking? There have been times that there have been things that have broken depending on region and other factors, but the resolution on the vast majority of them is very quick. I would say in recent months, I have rarely seen any major issues.

The support.powerbi.com site has a monitoring dashboard on the top that identifies any issues. you can also check in Office 365 admin.

Power BI is a Software as a Service, and as such, you can't control deployments of new versions/updates/etc.