It doesn't seem like it's possible to do it, no.
We have older floor plans that were exported to PDF, and when measured in Acrobat Pro the units are feet. Perhaps this option is just no longer available?
There's a bug, so you can get the numbers right but not the units.
First, make sure 'Embed scale information' is turned on for the Acrobat ribbon > Settings dialog.
That will ensure the units from the Model and Layout viewports are referenced in the PDF file (note this doesn't work with AutoCAD's own PDF export feature). If you have a 20-feet-diameter circle in the model, Acrobat will measure it as 20.0, but it won't say "20 ft".
The measurement scale only exists in the context of a viewport, so other areas of a layout (title blocks, borders, even the printed scale indicator block) will be seen as 1:1 in paper space. The scaling factors on Output Manager and for the viewport itself have no effect - the circle will measure as 20 'model unit things' even though the size on the printed page will change.