Finally found an → input plugin ← for WinAMP that plays AAC files (.m4a) encoded by iTunes (local mirror).
As far as I know, this plugin doesn't play protected files from the iTunes Music Store - for that you'll need the M4P input plugin.
03-11-24: This version seems to allow tag editing without corrupting the files.
Clarification: The input plugin linked from this page is compiled by John Edwards, from the source code produced by Menno Bakker. There is another compile from the same source by Case here. The plugin is also found as an executable at AudioCoding.com and RareWares. For more information and sources, see the SourceForge project page.