Sure. That is definitely possible. We really have no idea how ASI will act in any regard.

Maybe a natural part of having intelligence would include some degree of curiosity. Its not absurd to imagine a scenario where ASI will want to explore phenomena like blackholes, sample the material from neutron stars, etc.

In any case, if life is possible on even a couple of thousand other stars out of the 100 billion in our galaxy, it would also be possible that life/intelligence evolves in a similar way more than a handful of times. If each of these aliens create their own ASI, then all types of different scenarios would probably play out. I would imagine that wanting to secure itself from a singular planetary catastrophe and extinction event by spreading out would not be out of the question for at least one of these ASI entities.