Code will likely return at some point, depending on exactly what caused the valve to stick closed. The P2443 condition ("switching valve stuck closed") must be present for two consecutive driving cycles to trigger the MIL.
In the FJ's secondary air injection system, the air pump is turned on for a short time after a cold start to help the catalytic converters warm up more quickly. An air injection switching valve with an integral pressure sensor is located on each exhaust manifold. The pressure sensor is located upstream of the valve. When the valve is commanded to open, the ECU looks for exhaust pressure pulses, and if it sees none, it assumes that the valve is stuck closed.
If the stuck-valve condition somehow corrects itself, after some number of driving cycles the ECU will turn the MIL off, but that is no guarantee that the valve won't stick again.
Please keep us posted ... I'm very interested, as I have a '14 with 40K miles, and it has exactly the same SAI system.