For the Poll web part, there is a property "hide if closed", when that's checked, at least the poll will be hidden when it reaches the OpenTo time.
But there is nothing to trigger the Form webpart to be visible dynamically from the Poll. I tried to use {% WebPart.GetValue("Poll", "PollOpenTo") |(identity)GlobalAdministrator%} to see if I can get the date, but later find out the Poll webpart was created before Macro was introduced, so it won't work. You will have to customize the Poll webpart in order to expose some of those value to macro.