Unfortunately not, by the current game's settings.
ZOs already told us they are not going to use UI reader for skills and suchs tuff so maybe they ment the quest NPC texts neither
I think one can read them by API somehow, I can have a look as I find the time.
If tere is a way to get the text and use the UI reader to read it then I can add this to FCO Accessibility.
btw:
If you want to jump to any addon in your list you can use the slash command
/addons <addonName or parts of it>
or
/as <addonName or parts of it>
It will open the addon manager and search then.
Your cursor is then top right in the search edit field.
The first found result will be marked with a surrounding [> addon name here <].
Pressing the return/enter key jumps to the next search result.
I'm currently working on the UI narrator reading out loud the found addon name to you + the current enabled state.
And adding a keybind there at the addon manager to enable/disbale (toggle) the selected (by search, or below the mouse cursor if no search is
active) addon.
And I'll add another keybind, if possible, to start the addon search at the addon manager so it will clear the current search and let you directly type the next search string.
Hope this will improve handling for you so you can use the ingame addon manager too, or at least check an enabled state more easily.