In a way, this movie explores what it's like to be an ageless widow. Roughly around the time of her "immortality accident" was after her first husband died. One might say the movie is a metaphor for finding someone to move on with your life with. And Adaline didn't have another "immortality accident" until she decided she loved Flemming.
It may also be that fate wanted to give her another soulmate, even though he wouldn't be born for 80 years or so. So it decided to help her wait.
The title of the movie can be seen as a Stealth Pun about how old Adaline is when you consider the double meaning of "age" (an era/the number of years one has aged). Part of what drives the plot is Adaline trying to hide how old she is from both old friends and new people alike.
If Adaline gets a grey hair at the end, one of two things will happen. The first is that Adaline will age much faster than everyone she knows and be dead within a few years. The second is that her daughter, who is already in her eighties, will die before her.
The second one is pretty much written into the film. Adaline and Flemming have that conversation at dinner.