In my experience I've not seen this work. The only place you can changee a value of the properties is in a table such as BOM where you're given the option to keep link or break link befotre editing the field.
I think an annotation can only call the value from a part / assembly.
In your drawing template, you can define a Title Block. This would allow you to enter your custom properties in your drawing and they will show up in your part.
Search the help for "Defining or Editing Title Blocks"
Ridwan, like Tyler said, drawing titleblocks and BOM's have this capability to an extent, but you can't modify the underlying property of a regular drawing note, for example.
This would make an good enhancment request.
If you're using a good custom property automation macro within the part/assembly, I'd argue this would be a more efficient way of changing the properties than via the drawing sheet.