I obtained more info on the Japanese IME.  It has 2 modes of operation: 'romanji' and 'kana'.  In romanji mode, one types the ascii transliteration of the syllabic chars.  When one types type the syllable vowel , the program replaces the sequence of 1 to 3 ascii chars with a Japanese char.  So while typing 'akitsu', the 'a', 'ki', and 'tsu' would become 3 chars, with the 'k' and 'ts' momentarily visible.  Modifier combinations naturally work since the keyboard is being interpreted as outputting ascii chars.  In kana mode, japanese chars appear directly, but Ctrl must, in effect, temporarily revert the keys to their ascii interpretations.

A Chinese keyboard with a pinyan (romanization) input mode might do the same.  But non-English keyboards having an ascii mode is likely exceptional.  Given this and the two answers above, I conclude that delivering IDLE with a 'complete' set of IME-compatible keysets is an impossible problem.

I definitely want to document the problem.

I will stay open to the possibility of a 'customizer' that would prompt a user to hit all the character keys in a defined order and then augment an existing keyset using the method described in msg300716.  The table at https://www.tcl.tk/man/tcl/TkCmd/keysyms.htm suggests that this could potentially cover accented latin, cyrillic, greek, hebrew, arabic, and japanese keyboards.