The problem with your analogy is that the debris from the spaceship, etc. would still be visible to an observer after the fact. A better analogy would be this:
The aliens point a camera at our entire civilization. Ignoring the fact that this cloak works on the order of monumentally smaller scales than civilizations and the time it takes to put an ice chunk in a star, we use the cloak while we put an ice chunk in a star. The aliens would see our civilization jump from a state with no ice chunk in a star to one with an ice chunk in a star. Assuming that their measuring devices are up to the task, they would still be able to find all the spaceship debris, etc.
The problem with your analogy is that the debris from the spaceship, etc. would still be visible to an observer after the fact. A better analogy would be this:
The aliens point a camera at our entire civilization. Ignoring the fact that this cloak works on the order of monumentally smaller scales than civilizations and the time it takes to put an ice chunk in a star, we use the cloak while we put an ice chunk in a star. The aliens would see our civilization jump from a state with no ice chunk in a star to one with an ice chunk in a star. Assuming that their measuring devices are up to the task, they would still be able to find all the spaceship debris, etc.