Do the A2+s have an auto-sleep, idle, or auto-power-off function? Can I leave them on all the time?

The A2+ is equipped with a power-saving circuit that turns off the final stage of the speaker's amplifier when no input signal is detected, so you can absolutely leave them on when not in use. This activates right after you stop playing music, and is instantaneous (as soon as the input signal stops and it disengages automatically once an input in reintroduced), so there shouldn't be a noticeable delay when resuming audio. It's also fine to power off your speakers when not in use if you prefer.