As a former lifeguard and now MB, I would not be okay with this. I've worked with many well-meaning lifeguards over the years who had trouble staying focused on the pool, especially during an all-day shift in the heat. Even the best of them occasionally have to stop watching the pool as a whole in order to address inappropriate behavior or help someone in trouble, either in the water or on deck with a first aid issue. That creates a vulnerability, especially for a child as young as six, which is precisely why most pools do not allow children under the age of 10 or 12 to be on site without adult supervision.
If you were my nanny, I would expect you to be sitting on the edge of the pool, in a chair or otherwise, and watching/supervising my kids closely rather than looking up from your tanning session once in a while to "keep an eye on them." The lifeguard is there to prevent and intervene in emergencies; he or she is not in a position to fully supervise an entire pool full of kids.