Yes, very secure. The garage door is locked from the inside. The door to the room from the inside has a deep deadbolt and a handle lock.
I've got to say something about the Green Glue used inbetween the layers of sheetrock. I read tons of articles on this stuff and other solutions prior to purchasing because I was skeptical about it. It was expensive for one, just under $1000 US for the 6 cases of glue and the case of sealant, but the stuff works!
I added two layers of 5/8" sheetrock to all walls and ceiling. On the back of each sheet of rock I applied 2 tubes of Green Glue. Once the first layer was up I sealed all of the seams using acoustic sealant. Then added the second layer of sheetrock and Green Glue. The second layer was then taped and textured prior to painting. Once again, this worked wonders reducing the amount of sound that escaped the room, so much so that the room was really "live" inside, like an echo chamber. The sound panels have calmed it down considerably. I didn't want to completely deaden the room so some of the surfaces weren't treated.