Chris,
The answer is "maybe".
As Lori alluded to some aspects can only be determined by the "warm body".
The PDF Association did the heavy lifting for us to parse out the requirements.
These are available in the Matterhorn Protocol.
See:
http://www.pdfa.org/2014/06/matterhorn-protocol-1-02-now-available/
Consider - In clause 7.2 of ISO 14289-1 we have
"The most semantically appropriate tag shall be used for each logical element in the document content."
A PDF with all page content tagged / role mapped to the "P" (Paragraph) element could "pass" Acrobat's full check.
But, if the content unequivocally has a logical hierarchy containing an H1 then P content then H2 (and P content) and, again H2 with P content the PDF does not comply with ISO 14289-1, PDF/UA-1.
To have high confidence that one's output PDF are accessible PDF (ISO 14289-1, PDF/UA-1) then the following resources need to have "well worn pages" from having been used.
Have ISO 32000-1 on hand. Understanding clause 14.8 is essential.
To get a sense of what is coming obtain a copy of ISO/DIS 32000-2.
Have ISO 14289-1 on hand.
Have the Matterhorn Protocol on hand.
Be comfortablly conversent with
PDF/UA-1 Technical Implementation Guide: Understanding ISO 14289-1 (PDF/UA-1)
PDF/UA-1 Technical Implementation Guide: Understanding ISO 32000-1 (PDF 1.7)
Achieving WCAG 2.0 with PDF/UA
Visit AIIM for these.
http://www.aiim.org/Research-and-Publications/Standards/Committees/PDFUA
Additional, usefull tools.
The free PDF Accessibility Checker (PAC).
http://www.access-for-all.ch/en/pdf-lab/pdf-accessibility-checker-pac.html
Olaf's (Callas software) pdfGoHTML.
http://www.callassoftware.com/callas/doku.php/en:news:press:20121119
It may well be that, currently, the closest thing to a "turn key" product is Netcentric's Common Look product.
I suspect more robust options will be present post ISO 32000-2 / ISO 14289-2.
Be well...