For me, preparing my application was a good break from studying for the MCAT. If you have good time management skills, it's manageable. Obviously do not submit an application if it is not ready.
I worked on my application throughout the spring semester before I applied. I studied and took the MCAT on May 31st. I took the next week to finish and polish my application and submitted on June 7th. I was verified before the first group of apps went out.