Can the internal HD be the bottleneck?

I have a somewhat theoretical question.
Supposing that my internal HD is getting slow, or running slowly, if I were to stream from the external HD to my blu-ray player over the network, would that streaming be bottlenecked by the slower internal hard drive, or would it directly stream over the network as its own drive, without needing to pass through the internal drive? In other words, does the movie/USB drive get accessed over the ethernet directly, or does the internal HD mediate the process?
Supposing that my internal HD is getting slow, or running slowly, if I were to stream from the external HD to my blu-ray player over the network, would that streaming be bottlenecked by the slower internal hard drive, or would it directly stream over the network as its own drive, without needing to pass through the internal drive? In other words, does the movie/USB drive get accessed over the ethernet directly, or does the internal HD mediate the process?