@mec2015I feel it cuts both ways depending on the faculty. Obviously you need to find a faculty on which at least two or three sitting members share some of your research interests. Therefore, a program that has no one interested in your interests is a bad fit, no matter the reputation. On the other hand, programs do tend to look for diversity, and one would think that research interests somewhere outside the norm would be refreshing. As @olivialucilec noted, you never know, and the reality is that some schools probably take a more conservative approach and only align their candidates strongly to their faculty, while other schools have faculty that are intrigued by research that may go in a different direction from their own. To answer your first question, you probably are competitive, but acceptance rates vary as applicant pools do, so it is tough to say. You could always ask the admissions office how many applications they received this year and how many spots are open. I doubt they'd say at this point, but it couldn't hurt. Then you'd know your unweighted statistical probability.
I say this as someone who is wondering which side of that coin I'll fall. I am applying for a PhD. in Education, but my research interest is in Behavior Disability programs in urban settings. Suffice to say, this is not a mainstream Education interest, so while I think it's a fascinating topic, I'm relying heavily on the faculty of any school that accepts me to believe I am passionate enough to drive a good portion of my own research because not a lot of doors spring open the merits of this research topic alone. I feel like I am competitive otherwise: two MAs, interdisciplinary background, high GRE, and a recommendation from the director of a Pedagogy program at a University. But really, who knows?
My seven schools are: WashU, Northwestern, BC, NYU, Rutgers, CUNY Grad Center, and Montclair State (a smaller NJ school). Best of luck to you!