Not on the default one.

But if you download Picture Album screensaver you can.

I could be wrong but I believe the date/time and weather refresh and slightly move each time the picture changes. I watched it one day and to my eye it appeared to move but could just be my eyes playing tricks on me.

I use ariel dream its brilliant, you can turn clock and location off in settings if you want.

On my Shield, the chromecast app updated recently and you can now disable the time & weather display using the Home app device settings. However, the Chromecast-builtin logo still always displays.