In terms of the PDF/A standard there is nothing that would stop you from applying stamps to a PDF/A file.
In Acrobat X it is important to understand the PDF/A viewing mode implemented by Adobe – effectively in PDF/A viewing you cannot modify the PDF?A document. Applying a stamp implies modifying the document though….
In order to be able to modify a PDF/A document in Acrobat X, turn of the PDF/A viewing mode (Preferences -> Document -> View Documents in PDF/A mode – set to "Never"). Then apply your stamp.
Now comes the important part of this operation: it is key to ensure that the stamped file is still PDF/A conforming. Use Preflight to double check (Tools -> Print Production -> Preflight). Run a profile that reflects your PDF/A comformance level (a.g. for PDF/A-1b conformance run "Verify compliance with PDF/A-1b"). Usually it will turn out that your PDF file is PDF/A conforming.
If you want to continue to take advantage of the PDF/A viewing mode (good for protecting against unwanted changes of your archival files) go to Preferences and set the viewing mode for PDF/A files back to the "Only for PDF/A documents" value.