A superauto will grind, tamp and pull the shot for you. If you've been to Starbucks, that's the kind of machine typically in use. Yes, you can use fresh beans, but you will not have much if any control over the variables of grind, tamp, temperature, pressure, etc. If the machine does its job, it should be capable of decent espresso. Don indicates in his post above that the Saeco machine he uses does a nice job. I am not sure how much time you'll save, though. The machine must still be turned on and pre-heated, which typically takes 15 to 30 minutes depending on the machine. Many can be used with a timer, though, so that they turn on automatically each morning. The major benefit is automation.
I wish I could be of more help, but I have very little experience with super automatic machines. I owned one once several years ago, but only for a couple of weeks. I had issues with the grinder on mine and I traded it for a semi-automatic machine.
The video below may be of some help. It is a demonstration of a super auto made by Quick Mill that does in fact allow quite a bit of tweaking of the variables. I will ask around and see if I can find someone with more knowledge of the super autos and try to report back.
Best,
CaliforniaJed