The answer is this will happen if, not this will happen, and allow me to explain.
American culture is more assimilating and accepting than most European cultures, which are more homogenous. It's how this country was founded, and we have an extremely rich diversity of culture here. Contrary to popular belief, Islam is on the decline in the United States. Most Muslims who land here give up there old ways within 5 years, and by third (sometimes by the 2nd) generation you have completely assimilated Syrians, Afghans, Iraqis, etc who look, act, and behave just like your everyday Americans.
So where's the if here.
IF the United States fails to embrace new culture, then radical Islam will take root. If a culture is rejected, then they will not form an identity with the nation they live in, and if they do not find identity they live in, then they will find identity with something else, and that something else is typically not good. Ask yourself, why do so many European Muslims hightail it to Syrian to fight for ISIS? Why do so many Saudis travel to Syria to fight ISIS? What makes people pack their bags where they're at, pay large amounts of money to travel with the incredible effort involved, and settle roots in a foreign land and fight for a hopeless cause? It's not very logical, but it happens because they have no roots where they're at.
So the final answer is, if the United States fails to embrace and assimilate new cultures like it always has, then yes, you will see radical Islam on the rise here in America. If the United States embraces and accepts Muslims fleeing from the war of the Middle East, then they will assimilate themselves into our culture and be great citizens.
Don't build walls, build bridges.