The answer to your question is yes, but it doesn't work like you described in your example.
You cast the Nullify on the opponents creature. When he casts, not reveals an enchantment on his creature you must reveal your Nullify and decide if you want to pay the reveal cost and counter his enchantment. You do not get to look at his enchantment before you decide.
If he already had the Cobra Reflexes cast face down on his creature and then you cast a Nullify on it you would not reveal your Nullify when he reveals his Cobra Reflexes and he would pay the reveal cost to activate his enchantment.
I hope this helps.