It seems, to me, the said '...annotation texts...' are attributes of the INSERTED block (AcadBlockReference, in AutoCAD VBA term), not "MTEXT in Block" as the title of your post described.
Further more, it seems, the block (named as "FDS_xxxxxxxxxxxxxxxxx") itself DOES NOT DEFINED with attribute definition in it. Therefore, user cannot insert this block manually (with AutoCAD's "INSERT" command) with the attributes (annotation texts).
You may or may not know that attributes (attribute reference, not attribute definition defined in block definition) CAN BE ADDED to an inserted block (block reference). While this is not a normal way to insert block with attribute, but can be done with programming, but not with AutoCAD built-in "INSERT" command, nor from AutoCAD COM API (i.e. VBA code).
So, I would guess, this block comes with the "Factory Design Utility" and should only be inserted into drawing by that utility and automatically reset by that utility in certain conditions (as you said "...when you update the model...").
With VBA, you can move the attributes in the block reference. So, yes, after the the model updated, you can use VBA code to find the attributes in the block reference and move its position TextAligmentPoint property.
As for adding labels/dimension, you can add add Leaders/Text/MText/Dimension to the drawing, but they are simply separate entities, not part of the block reference as the attributes ("annotation texts").
Not knowing your VBA knowledge, I am not going into code details of moving attribute references in a inserted block.