It kind of depends on how much of your body is densely packed fat or muscle, but in a still pool I’ve never managed to float in a way that didn’t at least let me float with my mouth above the water.
I wouldn’t recommend anyone to go into the deep end of a pool without at least basic swimming skills, but if you can manage to remain calm, you can keep yourself from drowning pretty well, at least until help arrives.
If you can swim and want to try this out, please try not to look like a drowning person, or you’ll end up being dragged out of the water by a lifeguard (or at least get called out). The human body has an instinctive drowning response that doesn’t look at all like drowning people in the movies, and keeping your head just above the water can easily make you look like a drowning victim if you’ve got your arms side to side.