Pre-Service
If you live in a state that allows this pre-service career option, fully investigate it before enrolling. The big question is, Will this improve your chances of getting hired?
Perform your own mental "background check" of yourself first. If you have previously applied to an agency and not been hired, ask: Why? If you have baggage that is removing you from their employment consideration, address your baggage first. For instance, if you have bad credit, a poor job history, or do not meet some other requirements, address these flaws first. Most states will require some waivers, a background investigation, driver's history, and other requirements (physical and psychological screenings) before acceptance to an academy, and these can be very expensive.
Now, paying your own way to the academy is a double edged sword. First consider the tuition costs which can be very expensive. If you can find a scholarship or assistance, great; just remember you could have a loan to repay.
Secondly, most every academy has a caveat that while attending the academy there can be no secondary employment. So, how are you going to live these few months? If you are living with your parents or are independently wealthy then this is fine, but otherwise this can be very expensive. Some states experimented with part-time academy training, nights and weekends. This is dreadfully long and I am unsure if this is available any longer.