Processes vary from school to school. At some schools if you are placed on academic probation a notation is made on your transcript, at other schools it is not. At some schools students on academic probation are required to meet with their academic advisor or dean, At some schools being on academic probation means that you cannot apply for study abroad, pledge at frat or sorority, hold office, etc.
If money is an issue, your best bet is to check the policy at your school as policies vary from state to state and your status could affect any state aid that you receive.
Ex: In NYS if you are getting TAP, there are guidelines which consitiute successful progress toward a degree. If you do not meet those guidelines you are out of the money.
I think the same is true for students receiving Pell/SEOG. Satisfactory Academic Progress:
To be eligible to receive federal student aid, you must maintain satisfactory academic progress toward a degree or certificate. You must meet your school's written standard of satisfactory progress. Check with your school to find out its standard.
If you received federal student aid for the first time on or after July 1, 1987, and you're enrolled in a program that's longer than two years, the following definition of satisfactory progress also applies to you: You must have a C average by the end of your second academic year of study or have an academic standing consistent with your institution's graduation requirements. You must continue to maintain satisfactory academic progress for the rest of your course of study. http://www.ed.gov/prog_info/SFA/Stud...1998-9/it.html
Depending on the school if you have merit money, academic probation could (and ususally does) mean the loss of your scholarshipb ecause you did not live up to the terms of the scholarship.
Finals are approaching so dropping the class is a moot point. Are you missing any work? If yes, find out if your professor can give you an incomplete (which places your grade on hold until you turn in the rest of the work and it is evaluated. some schools will give you about 2 months into the spring term).