Amy Yvette Garrou, College admissions expert (US and international colleges)
I agree with all the other writers' responses. I would simply add that, to my knowledge, the only reason a college could rescind your offer of admission once they have approved your gap year is if you don't comply with the rules they have set for what you can do during your gap year. You should be sure you understand their conditions for approving your gap year; usually, they clearly state this in their letter or email to you approving your gap year.
For example, many colleges limit the number of credit hours you can earn during your gap year to less than one semester's worth (12 hours, for example). Essentially, they don't want you using your gap year to attend another college full-time.
Similarly, some of the most selective colleges say that you cannot use your gap year to apply to other colleges. How is this enforceable, you may be wondering? Well, your high school counselor is usually in the loop if you're asking your college for a gap year in April of senior year. That same counselor may receive your request to send College B and College C your final transcripts during your gap year if you apply somewhere else, and could (should) ask to see the conditions of your gap year before sending your transcript. Many college admission offices have strong relationships with high-school counselors (that's a good thing when you, the student, are asking a college for a favor, such as a gap year!) and may ask the counselor if they have any reason to doubt that you are obeying the terms of your gap year.
So the take-away is: Definitely ask for a gap year after you've been accepted to a college (in April of senior year); have a plan for your gap year; be aware of the college's conditions for your gap year; and be honest: hold up your end of the bargain, since they are holding a valuable place for you to enter a year later without re-applying.
Best wishes as you make plans!