We consider a Gaussian multiple-access channel where the number of users grows with the blocklength n. For this setup, the maximum number of bits per unit-energy that can be transmitted reliably as a function of the order of growth of the users is analyzed. For the per-user probability of error, we show that if the number of users grows sublinearly with the blocklength, then each user can achieve the capacity per unitenergy of the Gaussian single-user channel. Conversely, if the number of users grows at least linearly with the blocklength, then the capacity per unit-energy is zero. Thus, there is a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate per unit-energy is infeasible. The same observation was made by Ravi and Koch (Proc. IEEE Int. Symp. Inf. Theory, Jul. 2019) when the per-user probability of error is replaced by the joint probability of error, with the difference that the transition threshold is located at n/log n rather than at n. We further discuss the rates per unit-energy that can be achieved if one allows for a non-vanishing error probability.