This is already possible due to a an over-site in the code (with limitations), however I suggest that it is implemented as it is very useful.
The option "showOn" when set set to "none", displays no popup calendar or button (this works on the current version, it's sort of a hack).
This is very useful as some browsers have a built in calendar when the input is type="date" (like an iPad). Using modernizer the website designer can detect if the browser has its own datepicker ( if (Modernizr.inputtypes.date) { showOn= "none"; } ), and disable the jQuery UI calendar poping up, however it would be good to still be able to use all the functions associated with the datepicker (formatting, setting the date, alt-date, etc.).
This 'hack' currently does not work properly as datepicker does not work the same as a type="date" input.
This should also be the case for any other UI component where there could be a browser equivalent, like the upcoming timepicker as making them HTML5 compliant in setting the values seems a good idea.
To do this on the current datepicker would probably mean hiding the actual component and creating a cloned input inside the wrapper (the original input would in essence be the alt). There would also need to be an change hook attached to the original input.
I would do this myself, but snowed under at the moment. To be honest I do feel that this would is a minor priority as I don't think this would be a long lived useful feature because as browsers are developed, they will probably all have their own datepicker in the future.