In practice, you generally see the opposite. The "CPU" is in fact limited by memory throughput. (The exception is intense number crunching or similar compute-heavy code, where thermal and power limits come into play. But much of that code can be shifted to the GPU.)
RAM throughput and RAM footprint are only weakly related. The throughput is governed by the cache locality of access patterns. A program with a 50MB footprint could put more pressure on the RAM bus than one with a 5GB footprint.