your I-20 has a date when your F-1 start,

before that you still have to maintain your status, say J2.

Another this is your switch to F1 is just the "status", you will NOT have a F1 visa. Visa is only issued outside US. So you will not get a visa stamp on your passport, all you will get this way is a new I-20, prove you are of F-1 status. So you definitely have to maintain your J2 or other status before F1 become effective (not when you get the I-20 form).