Yes you can play the music while sequencing. LSP also has a cool feature that you can run the mouse over a section of the audio and you will hear that section. This makes it easy for picking transition points.
I'd recommend using your full months worth of trial to get the most experience with LSP before buying it. It also won't hurt that your 1yr/2yr of support won't start until later too.
There's a bunch of LSP training/webinar videos that Matt is putting together. They are probably worth looking at to make the transition form LOR to LSP easier.