Overlapping communications with computation is an efficient way to amortize the cost of communications of an HPC application. To do so, it is possible to utilize MPI nonblocking primitives so that communications run in background alongside computation. However, these mechanisms rely on communications actually making progress in the background, which may not be true for all MPI libraries. Some MPI libraries leverage a core dedicated to communications to ensure communication progression. However, taking a core away from the application for such purpose may have a negative impact on the overall execution time. It may be difficult to know when such dedicated core is actually helpful. In this paper, we propose a model for the performance of applications using MPI nonblocking primitives running on top of an MPI library with a dedicated core for communications. This model is used to understand the compromise between computation slowdown due to the communication core not being available for computation, and the communication speed-up thanks to the dedicated core; evaluate whether nonblocking communication is actually obtaining the expected performance in the context of the given application; predict the performance of a given application if ran with a dedicated core. We describe the performance model and evaluate it on different applications. We compare the predictions of the model with actual executions.