Is the output torque inside the gearhead rating?

Output torque is the motor torque multiplied by the reduction and by the efficiency of the train. The multiplication is trivial. The efficiency is not, and almost every torque surprise in a small gearmotor comes from treating it as a constant.

Efficiency in a small planetary or spur gearhead is a per-stage figure that compounds. A single stage at 90% is 81% at two stages and 66% at four. Published efficiency figures are typical values for the stage count, measured warm, after run-in, near the rated load. Three conditions move them a long way. Cold grease can double the drag torque of a small gearhead, which is why a mechanism that works on the bench at 22 °C can fail to start in a cold chamber. Light load makes efficiency worse, not better, because the fixed drag is a larger fraction of a small torque. And a gearhead that has never run has a higher drag than the same gearhead after a few hours.

The rated output torque of a gearhead is a limit, not an operating point. It is set by the weakest thing in the train, usually the output stage teeth or the output shaft and its bearing support, and it is a continuous rating with a separate, higher, momentary rating for shock. Sizing a configuration so that its calculated continuous torque sits at the rating leaves nothing for a jam, a cold start, or the stall that happens the first time somebody holds the output shaft. This tool warns below a 1.25 margin for that reason.

There is one asymmetry worth internalizing. The gearhead's rating limits what the mechanism may ask for, but it does not limit what the motor can deliver. A small DC motor at stall makes several times its rated torque, and through a high reduction that torque arrives at the output shaft multiplied. If the mechanism can jam, or drive into a hard stop, the gear train sees the stall torque times the ratio, not the number on this page. Either the drive limits current, or the mechanism has a compliant stop, or the teeth take it.

Back-driving is the mirror image. Torque applied at the output shaft is divided by the ratio and divided again by the efficiency in that direction, which is lower. A high-ratio planetary train is hard to back-drive but is not self-locking, so it will not hold a load with power removed. If the mechanism has to hold, that is a brake or a self-locking element, decided before the motor is chosen.