===Edit1 2018-09-11===
I came back to this old thread accidentally, and as I had analysed the task since again out of interest, and written and arranged some code for it, I now attach this demo containing that code. The main aspect was moved from the pdf files to the 'Draw' document that may or may not be created by opening a pdf. In fact the demo shows some graphic shapes created in Draw and containing text, some of them grouped...
The main enhancement is that now the DrawingDocument, its DrawPages, the ShapeColection(s) and the Shape(s) contained therein are recursively resolved. The contained text is collected first in an array together with information about the original position of the particular shape, and then sorted based on that information in advance of the output to a new TextDocument. Thus the order of text is no longer defined by the logical order of the shapes, but by the visual position basically. To do this even more precisely would require a few corrections to the coordinates of position based on the shapes' properties.
You may play with the example rearranging the shapes on the second slide and compare the results.
The included sorting algorithm was written from scratch. It isn't optimised concerning the sorting itself but reducing the number of needed transpositions. (It also is not optimised for the specific task where no transpositions at all would be needed.)
As always interested in criticism and suggestions.
(I personally never made much use of the proceeding.)
The code posted below is from my original answer. It was not changed during editing.
===Edit1 End===
Even when opening a pdf the way @Mike Kaganski pointed to, it will be "unmanageable" as he also told. In very rare cases where you urgently need to import the text content of a pdf without any formatting, you may open it in LibO Draw and then apply a "macro" collecting the texts.
Since simiiar requests reoccurred now and then I once sketched a very raw piece of code for the purpose in BASIC.
You may use it and enhance it as needed at your one risk.
REM ***** BASIC *****
REM Wolfgang Jäger (Lupp); 2016-09-05; Copyleft 0
Option Explicit
REM This procedure was sketched because questions about moving the textual
REM content from pdf files opened in 'Draw' into an actual text file come up
REM now and then, and there was not offered a solution yet, as far as I know.
REM
REM Of course, this provisional code cannot replace a thorough solution
REM to the problem (if actually needed at all).
REM In specific there is NOT MADE AN ATTEMPT TO RESOLVE GROUPS or to process
REM the 'Draw' objects regarding their position. The sequencing of texts goes
REM along the logical order of the objects.
REM For a PDF automatically imported by 'Draw' this should work.
Sub experimentalExportTextFromDrawToWriterDoc(optional pNum as Long)
Dim doc0 As Object, page As Object, shape As Object, shapeText As String
Dim doc1 ...
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