Acrobat (not Reader), Foxit, others I tried. It's not impossible, although the result may vary. PDFs, inheriting from PostScript, do have the concept of fonts

Acrobat (not Reader), Foxit, others I tried. It's not impossible, although the result may vary. PDFs, inheriting from PostScript, do have the concept of fonts and text strings, which can be edited. They're not just a soup of vector shapes.