I doubt it makes a difference. SSDs are an awful lot better at sequential writes than random writes, and concurrent IO would mainly speed up random access.
Besides, I don't think anyone really has a local network which is faster than their SSD. Even a 4-year-old consumer Samsung 970 Pro can sustain full-disk writes at 2.000M Byte/s, easily saturating a 10Gbit connection.
If we're looking at state-of-the-art consumer tech, the fastest you're getting is a USB4 40Gbit machine-to-machine transfer - but at that point you probably have something like the Crucial T700, which has a sequential write speed of 11.800 MByte/s.
The enterprise world probably doesn't look too different. You'd need a 100Gbit NIC to saturate even a single modern SSD, but any machine with such a NIC is more likely to have closer to half a dozen SSDs. At that point you're starting to be more worried about things like memory bandwidth instead. [0]
[0]: http://nabstreamingsummit.com/wp-content/uploads/2022/05/202...