Will Sagittarius A* eventually consume the Milky Way?
The short answer is no. The gravitational pull of Sagittarius A* is simply not enough to consume the Milky Way on its own. The laws of gravity are such that gravity doesn’t care about the object causing the gravitational pull, just about its mass.
If we replaced the Sun with a black hole with the same mass, and a radius of approximately three kilometres (1.8 miles), nothing would happen – besides us not getting sunlight anymore. Earth would keep rotating around the Sun as it does now, not knowing that the Sun has turned into a black hole as its mass has remained the same. To be consumed by a black hole, you would have to plunge straight into it, which is somewhat akin to finding a needle in a haystack.
Much more concerning for us is the fact that in less than 5 billion years, our Milky Way will collide with our neighbouring galaxy Andromeda, which at its centre hosts a supermassive black hole 100 times more massive than Sagittarius A* – therefore 100 times as large.
However, even in this extreme case the probability of this black hole swallowing the Milky Way is still pretty low.