It depends on the auto-update type.
For notification updates (a prompt displays advertising an update is available): Yes, user must have Admin rights to install the update
For Background Updates (Flash Player updates silently in the background): No, Background Updates uses the SYSTEM account to update Flash Player without any user interaction.
m_vargas thank you for the quick reply!
Can someone point me in the direction of some documentation to support this?
I'm actually not sure if this information is documented in a tech note, aside from the Background Update section in the Flash Player Administrator's Guide, page 20 "Performing a background update" refers to the task running as the SYSTEM user.
However, on Windows Flash Player installs to %WINDIR%\System\Macromed\Flash and %WINDIR%\SysWow64\Macromed\Flash (on 64-bit OS), and /Library/Internet Plug-ins on OS X, a such Administrator permissions is required in order to install Flash Player.