The battery is rated for 3A output, which would yield four hour life at max draw. Since your devices will draw less than that, you should be fine.
The FP24 current will vary quite a lot with phantom load and LED setting. Worst case phantom is 1W before conversion losses, figure the whole box isn't going to do worse than 2W, which is 0.4A from a 5V supply.
Shure gives you a hint of power draw on page 5 of the user guide: 2x AA alkaline is 6Wh, so their max draw at high load is 2 hours = 3W. Turn down the LEDs and don't use headphones, you are probably down to 2W.