In this paper, we propose a thorough analysis of an advanced binary tree algorithm with multipacket reception (MPR) capabilities, along with timeliness metrics such as age of information (AoI) and packet loss probability (PLP) in a gated access setup scenario. We consider a finite number of users with Bernoulli arrivals and leverage packet preemption capabilities in their buffers, highlighting a novel and significant aspect. Initially, we explore the expected length of the collision resolution interval, conditioned on the anticipated number of users who have arrived beforehand. Notably, the preemption of user packets occurs both inside and outside of the corresponding collision resolution intervals. Subsequently, we illustrate the state transitions of contending users, conditioned on the MPR scenarios. Due to the capability of employing MPR, the receiver can successfully decode all the packets in an error-free channel. Furthermore, we demonstrate that, in gated access, the normalized throughput increases with an increase in the upper bound of MPR capabilities. Nonetheless, delay, PLP, and AoI exhibit superior performance in the unnormalized case. This demonstrates that enhancing physical resource capabilities in the unnormalized case leads to improved performance in a random-access channel when using binary tree algorithms.