Sunny 16 is like a "sunny side up" fried egg. It's awfully easy to either undercook or overcook if you aren't careful.
So, will my photo be all slimy if it is under exposed?
On the question of smartphone apps--accuracy of the meter has more to do with the camera hardware than the app. Most of those apps just turn the camera on, and read out the auto exposure settings. So if it sees the camera set at f5.6 and 1/1000, and you've set the app for f16, it will just do the adjustment for you and tell you that 1/125 is the correct shutter speed. It sounds like the app that
@wiltw is using is allows you to add an offset to that conversion. Its possible some apps could build their own metering system by turning off auto exposure setting it to a fixed exposure, then pulling a camera image and doing averaging on the pixels, but those are still going to be dependant on the hardware.
One thing I wish that apps would have is the ability to display exposure using different aperture or shutter scales. Of course most/all handheld meeter only support a single scale as well, but an app would have a very very easy time displaying with older scales. I have a fair number of LF lenses in older shutters with both aperture and shutter speed scales that don't match the common 5.6/9/11/16/22 or 15/30/60/125/250/500 modern scales.