In HPC applications, one of the major overhead compared to sequentiel code, is communication cost. Application programmers often amortize this cost by overlapping communications with computation. To do so, they post a non-blocking MPI request, perform computation, and wait for communication completion, assuming MPI communication will progress in background. In this paper, we propose to measure what really happens when trying to overlap non-blocking point-to-point communications with computation. We explain how background progression works, we describe relevant test cases, we identify challenges for a benchmark, then we propose a benchmark suite to measure how much overlap happen in various cases. We exhibit overlap benchmark results on a wide panel of MPI libraries and hardware platforms. Finally, we classify, analyze, and explain the results using low-level traces to reveal the internal behavior of the MPI library.