How would the story be different if the man in the yellow suit had not died?What might have happened to the Tucks?

If the man in the yellow suit had not died, the Tucks would have continued their existence with no one knowing about them except Winnie.

When Mae Tuck kills the man in the yellow suit, the Tucks become on the radar of the local constable.  If this had not happened, there is no reason to assume anyone would have ever found out about them.  As it is, the constable does not know they are immortal. ...

If the man in the yellow suit had not died, the Tucks would have continued their existence with no one knowing about them except Winnie.

When Mae Tuck kills the man in the yellow suit, the Tucks become on the radar of the local constable.  If this had not happened, there is no reason to assume anyone would have ever found out about them.  As it is, the constable does not know they are immortal.  Winnie breaks Mae Tuck out of jail so they won’t find out when they try to hang her.

Mae Tuck explains to Winnie that the family has gotten adept at hiding what they are.  They live on the outskirts of the community, travel to different towns to sell their wares, and move on once they have been in a place for a decade or so.  This way, no one ever really gets to know them.

“… So Jesse, he does what strikes him at the moment, working in the fields, or in saloons, things like that, whatever he comes across. But they can't stay on in any one place for long, you know. None of us can. People get to wondering." (Ch. 10) 

She does not mean to kill the man in the yellow suit.  He was being very persistent about finding them. Once he did, he wanted to sell the spring water.  This worried and angered Mae, and she acted when he threated to use Winnie as a demonstration.  She hit him a little too hard, and the constable saw. 

The Tucks knew that if Mae was hanged, she would not be able to die.  This would give up her secret, and maybe the entire Tuck family’s.  For this reason, Winnie agreed to help break Mae Tuck out of jail so the Tucks could disappear and no one would ever know.

The one other possible ending would be that the man in the yellow suit would find the Tucks later, and force them to tell about the water.  That would be a very different ending, because he would try to sell it and everyone would know.