that depends. if you have installed launchbox in your user profile (C:\users\*your profile*) then yes, unless you give the other user account that will run launchbox rights to access that folder you will not be able to run the app.
This is probably not the case.
to my knowledge launchbox/bigbox wil not write data into your userprofile but will instead contain everything in it's own folder structure.
if you encounter issues running LB/BB with a different user you should check if the user has rights to the folder. (right clck folder, check security and see if the user has read/write or full control priviliges on the folder where LB/BB resides)
in other words it should not be a problem, and if so you can fix it.
this is about LB BB.. it is very possible that some emulators WILL write configs/saves into your profile.. some crappy emu's will even demand admin rights