The problem with streaming high-bitrate content like Blu-rays from a HDD is not the overall sequential speed, but the random access speed.
If you read from different files at the same time, it needs to seek around on the disc, move the read heads constantly - its just going to be slow.
Personally, i can't say i tested this extensively on actual BD movies, but from experience in similar situations, i would not expect more than 2 or 3 BD movies to work (if even that).
I've had issues myself when trying to watch a single movie while copying data onto the same HDD at full speed, was already enough to trip up playback.
I had to adjust my ripping workflow to directly rip onto the media storage network drive, instead of my local drive first, because writing at BD read speeds is OK, writing at full network copy speed is not.