Screensaver

No, that's not possible,

It might be possible to create a watchface that doesn't draw anything after a couple of seconds but there isn't a button you could use to make that watchface draw the time (and other info you might need). All buttons are already in use for other functions and cannot interact with a watchface.

Why you would ever want what you asked for is beyond my comprehension. There isn't a single useful reason to have a screensaver. 

Thank you Elbo, I was thinking about saving energy maybe but the main reason is that I prefer a black screen, I find my watch more beautiful like that! Thanks again for your response. Fred

Use a build in watchface. Do not use a thirdparty watchface if you want to save energy. The garmin ciq sdk is really bug infested and I even got a mail from garmin that it's best to avoid third party apps/widgets/watchfaces (because garmin is stupid enough to not build in features that prevent a third party app to *** up)

Just use one that is minimal, preferable without a seconds hard. But you're not going to notice any difference in battery life at all (unless you use a buggy third party watch face). The screen doesn't use much energy since it's not a amoled. gps uses the most, heartrate sensor is second (I think).