The current version of Google Chrome for Mac (14.0.835.202) is not correctly supporting this behavior, even when the System Preference to "Restore windows when quitting and re-opening apps" is selected in the General Preferences pane (like the Mail app or Safari does). There is an open bug ticket on this issue with Google so at some point the "remember full screen state after close" should be resolved. Here is the bug report link:

http://code.google.com/p/chromium/issues/detail?id=94611

(I removed the original script, but I couldn't come up with anything better than this either.)

set fw to front window
do shell script "open ~/Notes/todo.txt -Fa iA\\ Writer"
delay 0.1
tell application "System Events" to tell process "iA Writer"
    perform action "AXPress" of (button 1 where subrole is "AXFullScreenButton") of window 1
end tell
delay 1.5
activate fw

WriteRoom has an option to open documents in custom full screen windows. If it's selected, you could use something like open file.txt -Fjga WriteRoom.

If someone else just needs to open an application on the background, you can use open -jg or launch. launch sometimes opens a visible window if an application isn't open and open -jg if an application is open but has no windows.

set b to "com.apple.TextEdit"
tell application "System Events"
    if bundle identifier of processes contains b then
        launch application id b
    else
        do shell script "open -jgb " & b
    end if
end tell