Possible to script palette menus Save and Load Curves?

Question

Is it possible to script CS4 Photoshop's palette menus? Specifically, the "Save Curves Preset ..." and "Load Curves Preset" ... of the Adjustments Palette.
I have 600 images, some of which have layer>new adjustment layer>curves applied.
I want to save the curves using the image name. Later, I want to be able to load the appropriate curve.
E.g., for image001.tif, the curve would be image001.acv
(I already have a loop set up to iterate through the files and get the file names.)

Answer 1

Thank you.
I got both scripts working without JS or AS errors, but, when trying to load .acv files generated by the second script, CS4 Photoshop gave an error:
"Could not load the curves because the file is not compatible with this version of Photoshop"
(The loading script works fine when loading .acv files created directly from Photoshop.)
The only change I made to your Save Curves code was:
FROM: var myACV = new File('~/desktop/myCurve.acv')
TO: var myACV = new File(file);
and made the code a function:
saveCurves(file)
YOUR CODE HERE
so that I could incorporate it into the Applescript.
Maybe that was naive (I'm not very knowledgeable about JS).
Here are the scripts I'm using:
SAVE CURVES:
set gammaFolder to "/Users/me/Desktop/myproject/gamma/"
tell application "Finder"
          set TheFolder to choose folder
          set FileList to every file of entire contents of TheFolder as alias list
end tell
repeat with theFile in FileList
          set thefilename to theFile as string
          set text item delimiters to ":"
          set thefilename to last text item of thefilename --remove path
          set text item delimiters to "."
          set thefilename to first text item of thefilename --remove extension
          tell application "Adobe Photoshop CS4"
  activate
  open theFile
                    tell current document
                              if exists layer "Curves 1" then
                                        set current layer to layer "Curves 1"
                                        do javascript "saveCurves('" & gammaFolder & thefilename & ".acv');
function saveCurves(file) {
-- SAVE CURVES JAVASCRIPT HERE
};" --show debugger on runtime error
                              end if
                    end tell
          end tell
end repeat
LOAD CURVES:
set gammaFolder to "/Users/me/Desktop/myproject/gamma/"
tell application "Finder"
          set TheFolder to choose folder
          set FileList to every file of entire contents of TheFolder as alias list
end tell
repeat with theFile in FileList
          set thefilename to theFile as string
          set text item delimiters to ":"
          set thefilename to last text item of thefilename --remove path
          set text item delimiters to "."
          set thefilename to first text item of thefilename --remove extension
          set acvFile to gammaFolder & thefilename & ".acv"
          tell application "Finder" to set acvExists to exists my POSIX file acvFile
          if acvExists then
                    tell application "Adobe Photoshop CS4"
  activate
  open theFile
                              tell current document
                                        if not (exists layer "Curves 1") then
                                                  do action "Create Curve Layer" from "MyActions"
                                        end if
                                        set current layer to layer "Curves 1"
                                        do javascript "loadCurves('" & gammaFolder & thefilename & ".acv');
function loadCurves(file) {
-- LOAD CURVES JAVASCRIPT HERE
};" --show debugger on runtime error
                              end tell
                    end tell
          end if
end repeat