Only within each section; the list as a whole isn't necessarily alphabetical. Genie puts its "recommended" experiences at the top and then lists the rest in a different section titled "Other Experiences to Consider", so the attractions get broken up into multiple lists.
Maybe on iPhone it does. Unfortunately, the Android version does not appear to refresh when I click "Tip Board."
The fact that at least one version has a way to refresh without losing your place gives me some small sliver of hope that all versions will eventually have that ability, though.