If I were you I would submit the AMCAS application as soon as you are able to. This information can be found on the AAMC/AMCAS website. When I applied (4 years ago), you didn't need to wait for your MCAT scores to be available (not sure if this has changed); you could submit your application and then when the scores were available they would be attached to your application.
It was my understanding that AMCAS doesn't "send" out applications. Rather, med schools log on and retrieve applications for applicants interested in their program.
Regardless, many schools dont look at the "release date" or the date they were sent your application, they look at the date an application was submitted or complete. If a program you are interested in is more concerned with the submission date, then early is better. If the program you are interested in is more concerned with the completion date, then there is nothing you can do since the score release date is fixed. So an early submission can only help you.
Hope this helps. Good luck.
