There's no way that I know of to hide the box around the ActiveCell. However, you can create the same end result by placing the ActiveCell off screen (out of site of the user) and scrolling to the section of the screen that you want the user to see.
Cells(1000, 10000).Select 'Selects a cell that's far from the working area
ActiveWindow.ScrollColumn = 1 'scrolls to Column 1
ActiveWindow.ScrollRow = 1 'scrolls to Column 2
Now you've got a nice clear sheet without the selected cell box cluttering things up.