Hyperdimensional computing (HDC) is an emerging computing paradigm that represents, manipulates, and communicates data using long random vectors known as hypervectors. Among different hardware platforms capable of executing HDC algorithms, in-memory computing (IMC) has shown promise as it is very efficient in performing matrix-vector multiplications, which are common in the HDC algebra. Although HDC architectures based on IMC already exist, how to scale them remains a key challenge due to collective communication patterns that these architectures required and that traditional chip-scale networks were not designed for. To cope with this difficulty, we propose a scale-out HDC architecture called WHYPE, which uses wireless in-package communication technology to interconnect a large number of physically distributed IMC cores that either encode hypervectors or perform multiple similarity searches in parallel. In this context, the key enabler of WHYPE is the opportunistic use of the wireless network as a medium for overthe-air computation. WHYPE implements an optimized source coding that allows receivers to calculate the bit-wise majority of multiple hypervectors (a useful operation in HDC) being transmitted concurrently over the wireless channel. By doing so, we achieve a joint broadcast distribution and computation with a performance and efficiency unattainable with wired interconnects, which in turn enables massive parallelization of the architecture. Through evaluations at the on-chip network and complete architecture levels, we demonstrate that WHYPE can bundle and distribute hypervectors faster and more efficiently than a hypothetical wired implementation, and that it scales well to tens of receivers. We show that the average error rate of the majority computation is low, such that it has negligible impact on the accuracy of HDC classification tasks.