As a slightly computer literate native speaker of American English I find the sentence a little confusing. "Parties" usually refers to a group of PEOPLE. You say there is ONE device (a network device) which in turn may have multiple connections. Since the sentence is NEGATIVE (will not provide power savings) why not just say:
" Computers or any connected device set to standby mode will not provide significant power savings. "
Using the same word to refer to the same component helps the less sophisticated computer users when you are writing computer manuals. You only need a variety of terms when writing novels!