My question is based on the following assumption: Faculty members sit together and pick a few candidates each, from the pool of applicants. The faculty member who contacted me had picked me.
As Buffy said, in the US, candidates are normally chosen by committee, and there is no one-to-one matching between students and advisors. This is different than the situation in Europe.
Therefore, if I reject his offer, I would not be considered by the other faculty members, because they have already picked other candidates.
Things will vary widely across academia, so it is hard to give general advice (and I'm not familiar with EECE departments, so take my advice for what it's worth). But the committee does generally try to ensure some rough alignment between the students' interests and the department's needs. It could be that the department is only interested in you because you seem like a good match to this project / advisor, and so declining this project would probably result in your not being admitted. Or it could be that they really like you and are offering you this opportunity on top of a forthcoming admissions offer. It is really impossible to say what they might be thinking, but it's certainly possible that rejecting this offer could reduce your odds of admission.
If I am interested, an interview could be set up to discuss things further. However, I am not interested in this topic at all.
Still, I'm not sure any of this matters. You are not interested in the project, and getting an offer of admission based on your willingness to work on this odious project would not be very useful. So, I recommend being straightforward with them: perhaps you are willing to meet with the professor and discuss further, but your initial reaction is that the project doesn't seem like a strong match to your skills or interests. If this means they don't admit you, that's better than getting admitted but not being able to find a suitable advisor once you're there.
By the way, you might want to keep an open mind with respect to the project. Sometimes working on a less interesting project with an awesome advisor is worth it. And sometimes apparently uninteresting projects turn out to be connected to things you are interested in.