That depends on the number and size of files which you are transferring. For example, if you have 10 files which require 10 minutes each to transfer, then 10 threads running simultaneously will indeed provide a performance boost. If, however, you have 10 files which take 1 second each to transfer, then the connection setup cost is likely greater than the transfer cost and multi-threading makes no sense.
There are some other considerations, such as socket and memory usage, if the number of files is large, though they are easily managed by limiting the number of threads.