The short answer is yes, you could go ahead and study and test for your CDL without going to school or a company-sponsored training program.
The more accurate answer, however, is yes, but you won't be able to find a company that will hire you to drive for them.
You could study for and pass your permit test, using our program, of course, and then hire a truck for the driving skills test. Keeping in mind that you would probably need to also pay for practice time beforehand.
No, probably not. Most companies, because of insurance and policy reasons, will require new drivers to have attended and graduated from an accredited school providing at least 160 hours of instruction time.