Move a note along with the current date

Is it possible to attach a note on the date line so it moves with it as the “date now” is updated?

A symbol with a symbol constraint will move along with the current date. Here is what you need to do:

Add a symbol to your schedule.
Add the note (or symbol text).
With the arrow tool, double-click the symbol (on the schedule).
On the Constraints tab, for Constraint Type choose: Initialize to current date of schedule. The symbol will now "stick" to the current date as the current date changes.