There's no harm in applying. Several students in my PhD program took a year off after undergrad and worked in a university research lab as a paid assistant. Some said that they got into some grad programs after university, but they wanted to get a better research background that would help them get into a more prestigious school.

I suppose it's too late now, but to really distinguish yourself for some top-tier universities, you'll probably have to show evidence that you've pursued research or self-study (e.g. summer programs, indep study/research classes with a professor, personal projects, internships, etc.).