Not really. You will wake up around 4am in the morning and will have appointments and training for the entire day until lights out around 9pm. Depending on your MTI and whether they stay in the dormitory at night or not, you may be able to use your flashlight to sneak in some letter reading/writing time in your bed after the lights are out, but then you will be sacrificing sleep in order to do that and sleep is a very precious commodity at BMT.
Depending on how nice your MTI is and how well your flight performs, you may also occasionally get "patio breaks" during BMT which is when the MTI lets you go down to the dormitory patio and use the phones and buy junk food from the snack machines. The MTIs will use this as a punishment (Get this right, or lose your patio break!) so you may get more breaks if your flight performs really well. Your MTI may also release you to explore the base for a few hours, usually on a Sunday when you don't have a lot of appointments scheduled. This will normally be towards the end of training when you are getting close to becoming the senior flight. You'll be able to walk to the mini-mart and buy food and candy, buy food at Burger King, read magazines, use the internet, etc.
Just keep in mind these breaks are very rare and are by no means guaranteed. It's completely up to your MTI whether you get them or not and how many. It's best to go in to BMT expecting to not receive any at all and just count it as a bonus if you get one. Also keep in mind if you do get a break and someone returns to do the dorm late or screws up some other way, expect the entire flight to pay for it and to probably not receive any more breaks. Keep each other in line!