That the board is powered on is signalled by the +3.3V line, which is available on the headers.
The Bela running LED's (the one that blinks blue when the project is running) are also available on the headers. These are bicolor LEDs, they would turn red when an underrun occurs.
BelaMini:
P1.02 blue LED
P1.04 red LED
Bela cape Rev C:
P8.34 and P8.38 (not sure which is red which is blue)
Gem:
P2.02 and P2.04 (not sure which is red which is blue)
Additionally, Gem has a second "status" LED, which goes solid blue as soon as the board is powered (at the same time as +3.3V goes high), then it starts blinking when Linux has booted. The signal for this is available on P2.08 .
You can even change its behaviour at some later stage, for instance set it always off when the IDE is up and running.
All of the above signals are already present on the headers and won't take up one of the Bela digital outputs.