This paper studies the throughput scaling of wireless networks over channels with random connections, in which the channel connections are independent and identically distributed (i.i.d.) according to a common distribution. The channel distribution is quite general, with the only limitations being that the mean and variance are finite. Previous works have shown that, when channel state information (CSI) of the entire network is known a priori to all the nodes, wireless networks are degrees-of-freedom limited rather than interference limited. In this work, we show that this is not the case with a less demanding CSI assumption. Specifically, we quantify the throughput scaling for different communication protocols under the assumption of perfect receiver CSI and partial transmitter CSI (via feedback). It is shown that the throughput of single-hop and two-hop schemes are upper-bounded by respectively, O(n1/3) and O(n1/2), where n is the total number of source-to-destination pairs. In addition, multihop schemes cannot do better than the two-hop relaying scheme. Furthermore, the achievability of the Θ(n1/2) scaling for the two-hop scheme is demonstrated by a constructive example.