After you've rolled the dice once, and looked or thought about looking, there is no longer any chance for the condition "one 2 or two 2's". Except for seeing one die showing a 2, and not seeing the other one. The specific roll - any roll, each is specific - will settle on EITHER the one 2, or the two 2's, without question of which. Quantum mechanics doesn't extend into the macro realm, in which we reside 100% of the time.
You can't roll out the chart! Especially, not before the dice. Nor stand there thinking about this before doing either to not commit yourself.
__________________________________________________
Beyond this, intuitively, there is no rational way to equate "one 2 or two 2's (as an unknown)" and "rolls of one 2, plus rolls of two 2's (= 11)". Or's and and's aren't the same thing.