In answer to the question: Key bindings in i3 are a list of modifiers (Control, Shift, Mod1 - Mod5 and Mode_Switch) plus a keycode or keysym. A defined binding has to be matched exactly by the pressed keys for i3 to act on it. So in this sense every key of a binding really is required. Also if more modifier keys are pressed, i3 will ignore the combination completely unless it, too, is bound.
As for the problem described. I did some testing, but could not reproduce the described effect. So this does not seem to be a problem with i3 in general. Two things come to mind:
Your Mod4 key does not work at all. Could test with xev -event keyboard if pressing the <Mod4> actually does anything. (Note: it is possible to bind single modifier keys in i3 by using bindcode. This would prevent xev (or any other program) from catching the key, but it does not lead to <Control>+<Mod4>+a to be interpreted as <Control>+a (at least on my computer).)
One or more of your programs behave strangely and accept <Control>+<Mod4>+a as substitute for <Control>+a or ignore <Mod4> completely. Could you give a list or at least some examples of programs with which you have the problem?
Also, what does happen if you do bind <Control>+<Mod4>+a to something in i3?