Even though it says the effect is equivalent to a spell, it's still a supernatural ability. When you activate it, you are using a supernatural ability, not casting a spell (and thus don't have spell failure or AoOs or anything else that comes with spellcasting). My strict RAW reading is thus that no, those abjurant champion abilities wouldn't work, because they only work when you "cast a spell".
My common sense ruling, however, is that they should work, because abjurant champion enhances your self protection magic and this is magical and protects you.