No, an AR (ArmaLite Rifle) cannot shoot without a buffer tube. The buffer tube is an essential component of the AR-15 and AR-10 rifles, which are the most common variants of the AR platform. It is part of the firearm's recoil system and houses the recoil buffer and buffer spring.
When a round is fired in an AR, the gas from the fired cartridge propels the bolt carrier group backward against the buffer spring. The buffer spring then pushes the bolt carrier group forward, chambering a new round and preparing the firearm for the next shot. This cycle of operations is known as the firearm's recoil operation.
The buffer tube provides the necessary space for the buffer and buffer spring to function properly. It also serves as a housing for the recoil system and provides attachment points for the stock or other accessories. Without a buffer tube, the recoil system would not have the necessary components to function, and the firearm would not be able to cycle and fire subsequent rounds reliably.