ID is not science because there are questions it does not attempt to answer? By that same logic, evolution cannot be science either.
No, it is not science because "some unspecified entity doing X with unknown methods and for inscrutable purposes" is compatible with any observation, i.e. it doesn't explain anything.
The ToE predicts a nested pattern and indeed we do observe a nested hierarchy which can be arrived at using multiple lines of evidence.
ID on the other hand is compatible with a nested pattern as well as with any other pattern. Now if we had a model of this designer which makes certain predictions about what we should and especially shouldn't observe that would be a completely different situation but ID-ist try very hard to not specify this designer.