The paper investigates the problem of maximizing expected sum throughput in a fading multiple access cognitive radio network when secondary user (SU) transmitters have energy harvesting capability, and perform cooperative spectrum sensing. We formulate the problem as maximization of sum-capacity of the cognitive multiple access network over a finite time horizon subject to a time averaged interference constraint at the primary user (PU) and almost sure energy causality constraints at the SUs. The problem is a mixed integer non-linear program with respect to two decision variables namely spectrum access decision and spectrum sensing decision, and the continuous variables sensing time and transmission power. In general, this problem is known to be NP hard. For optimization over these two decision variables, we use an exhaustive search policy when the length of the time horizon is small, and a heuristic policy for longer horizons. For given values of the decision variables, the problem simplifies into a joint optimization on SU \textit{transmission power} and \textit{sensing time}, which is non-convex in nature. We solve the resulting optimization problem as an alternating convex optimization problem for both non-causal and causal channel state information and harvested energy information patterns at the SU base station (SBS) or fusion center (FC). We present an analytic solution for the non-causal scenario with infinite battery capacity for a general finite horizon problem.We formulate the problem with causal information and finite battery capacity as a stochastic control problem and solve it using the technique of dynamic programming. Numerical results are presented to illustrate the performance of the various algorithms.