That would be a bad thing, too much juice for a one-level dip. But check the last line of Continued Study, which states "He does not learn these features if he did not already know them." Since the iconic abilities are all granted at level 5 (except for Sense Void, at level 6), you'd need five levels in another class to pick up a second one.
Maybe I need a less wordy way to write this. What I'm trying to say with it is "You probably have one of the iconic abilities on this list. If you have it, you continue advancing it." Maybe I should say "If you already have features VWXYZ, your levels in master of elements stack with levels in classes ABCDE for the purpose of advancing those features." Better?
If they take Elemental mastery, and gain one of the other classes features, do you want them to use their full character level, or their master of elements level + class ABCD or E level?