Since the Amish tend to keep themselves isolated from modern society and avoid modern conveniences, it will be more difficult for them to prosper. They will have to put in more effort to thrive and avoid hardships, and this will likely keep their population in check. For this reason I think they would not become a major demographic.
I can't imagine that, in the 21st Century, many people will be aware of all of our modern technology and choose to give it up. I don't judge people who choose that; I actually have a lot of respect for them. It's just that all of these advances make life easier, and most people have become dependent on them. I would imagine that the birth rate is higher than average among the Amish, so it's possible that the population will grow. However, I don't think that many people will choose that kind of life, given a choice.
I do not believe that the Amish will become a major demographic because they do not draw attention to themselves. Of course, new family members will increase the size of the community and a few individuals may decide to convert to become an Amish person, but I do not believe that these reasons will be a huge impact that will make the Amish a large demographic anytime soon.
The self-imposed isolation of the Amish people is enough to ensure that despite their high birth-rate statistics that they will never be able to enlarge naturally as a demographic group. The Amish are also not evangelists which is another bar against them increasing their numbers substantially. While the number of people who choose to leave the Amish community for the 'English' world are small, they are still significant enough to depress the population figures.