Should I insert a colour bar if arbitrary units are used?
I would definitely include the color bar.  It just makes things easier to read, since you can compare the displayed values directly with your eyes, rather than having to refer back to a written explanation.  The bar also lets you see how the colors shade into each other as you move along the scale.

If it seems awkward to have the color bar in arbitrary units, you can explain exactly how you came by the arbitrary units (such as "data scaled by the maximum deviation from zero").  Then you can give the bar scale a more quantitative meaning.  Or, you might go the other direction and just labels the ends "low" and "high."