Yes you will need to have admin rights to install Studio.
You can use Studio in a non-admin account. The only exception is in Windows XP. If you are using Windows XP you may get a "No disc writer device available" error when attempting to burn a disc. In this case you can resolve the problem by following the instructions in this FAQ:
Error: 'No disc writer device available' in Studio when using Windows XP with a non-admin account