Are you able to use Acrobat.com to create Accessible PDF files

An "accessible" PDF is one that is ISO 14289-1, PDF/UA-1 compliant.

While the online service an provide a starting  framework of tags any content much more than "Hello World." will not be PDF/UA-1 compliant.

Compliance is rather critical. PDF/UA-1 is the "WCAG" for PDF.

As Sara mentioned to move a PDF into PDF/UA-1 compliance you will have to use Acrobat Pro (Any "Pro" from 6 up but XI is what is available today and compatible in contemporary OSs).

Resources you will need:

At AIIM:

http://www.aiim.org/Research-and-Publications/Standards/Committees/PDFUA

At the PDF Association.
(The PDF/UA  Reference Suite and the Matterhorn Protocol). 

PDF/UA Competence Center | PDF Association

Review Acrobat Help re: the accessibility checker - you need to use it and to do this effectively you need to understand what it does (and does not) check.

As  well, also (not exclusively ... it is "also") use PAC 2.
Fetch its "help" and read for understanding.

http://www.access-for-all.ch/en/pdf-lab/pdf-accessibility-checker-pac.html

At Adobe:

Acrobat Help | Accessibility features in PDFs

   (which has links to additional resources)

At your convenience browse this read-only forum:

https://acrobatusers.com/forum/accessibility/   

Be well...