I wrote a short AppleScript to take care of the issue. Note that the script does not check for updates itself but relies on OS X's checking it in the background so it requires that the options to check for updates periodically and download updates automatically be checked in the Software Update preference pane.
Create the following script in the AppleScript Editor and save it as an application:
-- A script alerting non-administrator users about available downloaded -- software updates set updates_no to do shell script "defaults read /Library/Preferences/com.apple.SoftwareUpdate LastUpdatesAvailable" if (updates_no > 0) then try set dialogResult to display dialog updates_no & " software update(s) are avalaible. Launch Software Update?" if button returned of dialogResult = "OK" then ignoring application responses tell application "Software Update" to activate end ignoring end if on error number -128 -- The user canceled so do nothing end try end if
From now on, whenever you login into that account *after* the automatic check downloaded new updates, a dialog bode informing you of the updates and suggesting to run Software Update for you is displayed. Of course, an administrator password is still required by Software Update.
This Script has been tested on Mac OS X 10.7.2 and detected the downloaded iTunes 10.5.3 update.
[crarko adds: I didn't have any updates available to try this with.]

