Yes, a motorcycle can stand up at a stop without the need for the rider to put their feet down to balance it. This ability is known as "balancing" or "holding the bike upright." Motorcycles, especially larger ones, are designed with a low center of gravity and a balanced weight distribution, which helps them maintain stability when stationary.
When a motorcycle is in motion, it relies on forward momentum and the gyroscopic effect of the spinning wheels to maintain stability. However, at a stop, these factors are absent, and the rider needs to employ techniques to keep the motorcycle upright. This involves using the rider's body positioning, control of the handlebars, and minor adjustments of the throttle and rear brake to maintain balance.
It's important to note that maintaining balance at a stop requires practice and skill, particularly for new riders or those operating larger or heavier motorcycles. Novice riders may find it more comfortable and secure to put their feet down at stops until they gain more experience and confidence in balancing the bike.