Should I take my school's Engineering class? (...)

If you don't take the class what is your alternative? You said you'd take time off, does that mean you would just not have a full course load and could end your school day early? Or would you be filling in the extra time with something else.

I think you should take the class. Being frank though, I don't think it will make or break your application but I do agree with @Melokenzie that it may raise some eyebrows. If your alternative is just having free time to chill, while tempting, it's probably not the best choice. Now, if you were going to have extra time and you planned on filling that time with an EC or a personal engineering project or something then I might consider not taking the class.

I feel like you should take the class because it shows that you actually care about engineering. Because if I were a college admissions officer and I saw that your school had an engineer in class and you didn't take it even though you were applying for the engineering major in my school I would be confused. If you feel that not being a P is going to affect you severely explain that you took it because you wanted to learn more about engineering as you wanted to be an engineer and there was no AP engineering available at your school.

I can't say how much it would help but it would cause them to question why you didn't take engineering if it was offered to you. That is what my counselor said. I want to study criminology and psyche both which my school offers. both are standard classes but it would look weird if I said those are my intended majors but didn't take any classes on them if I could. I get wanting a break but if selective schools are your targets that is not likely to happen.