Hypotheticly yes, but you would need something very big to block the light or reduce it. Planet sized for example, this is one way we detect planets around other stars, by measuring how much the light dims.
Another potential problem is that (at leas according to this wikipedia article https://en.wikipedia.org/wiki/List_of_nearest_galaxies) the closest galaxy is around 33000 light years away. So any signal we send will take 33000 years to get there and any potential return would take the same amount of time, so 66000 years in total. That is far longer than any human civilization exists