Yes Tricare does cover for I believe 120 days after separation. I was almost in the same position last year. My wife was pregnant during my MEB and I was worried about the same thing. I asked Tricare and they told me once you outprocess through MPF go immediately over to Tricare and reaplly for tricare prime through the TAMP program.
Transition Assistance Management Program - Military Benefits - Military.com
I guess lucky for me I didnt have to use it because of return to duty but then again i got shafted on the MEB and going through MEB again this year.