No, both shift keys and enter seem to be mapped to the compose key, which surprised me.
I thought I remembered a command line to map the compose key, but I can't find it right now. And thanks for reminding me what the pandora's compose key is!
It isn't possible to change the 'type' of a key using xmodmap. https://pyra-handheld.com/boards/threads/xmodmap-help-needed.77160/#post-1371239 provides a full xkb map file that should allow you to do what you want (note that 'Compose' is named 'Multi_Key'). Setting type of <RTRN> to 'PC_CONTROL_LEVEL2" should do the trick.