We consider online power control for a K-user energy harvesting multiple-access channel (MAC). We show that a simple online power control policy that requires each user to know only the mean of its own energy harvesting process and does not require any information regarding the energy harvesting processes of the other users is near optimal for any joint distribution of the energy harvesting processes and for arbitrary battery sizes at the K users. In particular, for any parameter values this strategy achieves a throughput region which is within a constant gap to the capacity region of the classical additive white Gaussian noise (AWGN) MAC. When the number of users in the MAC becomes large, the gap becomes negligible. Therefore, an interesting consequence of our result is that in the limit when the number of users becomes large, the sum throughput of the online energy harvesting MAC approaches the sum capacity of the classical AWGN MAC. While it has been known that the online throughput of an energy harvesting system can approach the AWGN capacity in the limit when the battery size goes to infinity, it is interesting that the AWGN capacity can be also approached in limit of large number of users.