Yes :)
You don't have to have played any at all on here, and you can still enter the FEN or PGN of a game from elsewhere, or you can enter the moves manually yourself. Either way you can still use the arrows and highlight squares.
Click on the New Game tab, there is a drop down box at the top showing a preset game time. Use that drop down. At the bottom of the list of preset times it shows Analysis. Click on that.
A box appears asking you to enter game details (like name of analysis board / player names) - optional.
Click on start analysis and your whole analysis area opens up for you
Is there a way to enter the analysis mode in Live Chess without completing a game, so that I can use it to view previous games?
Specifically, the ability to draw arrows and highlight squares with the right mouse button is what I'm after.