Graphene is a promising material which has been proposed to build graphene plasmonic miniaturized antennas, or graphennas, which show excellent conditions for the propagation of Surface Plasmon Polariton (SPP) waves in the terahertz band. Due to their small size of just a few micrometers, graphennas allow the implementation of wireless communications among nanosystems, leading to a novel paradigm known as Graphene-enabled Wireless Communications (GWC). In this paper, an analytical framework is developed to evaluate how the channel capacity of a GWC system scales as its dimensions shrink. In particular, we study how the unique propagation of SPP waves in graphennas will impact the channel capacity. Next, we further compare these results with respect to the case when metallic antennas are used, in which these plasmonic effects do not appear. In addition, asymptotic expressions for the channel capacity are derived in the limit when the system dimensions tend to zero. In this scenario, necessary conditions to ensure the feasibility of GWC networks are found. Finally, using these conditions, new guidelines are derived to explore the scalability of various parameters, such as transmission range and transmitted power. These results may be helpful for designers of future GWC systems and networks.