No, the output of powersupplies doesnt come on with the PC, its just a passthru and seldom found on current power supplies.
I would connect the 5v up to the speaker and try it off a different source - isolated like an ipod or one of those old things that spins CDs and plays, that way you can decide if they work well enough on the reduced voltage.
Then to see if its ok to plug into the computer you want to check for voltage between the 3.5 mm plug's sleeve and the chassis of the computer - there should be zero volts or close enough to it, if there is zero volte - plug it in - if you get 2.5v or so then you have a virtual ground in the speaker and its a lot of work to get it to work and not worth it.
Then see if you end up with any noise as a result of a ground loop - if none, then well done, your finished