Well, for instance, when I'm troubleshooting rules that aren't working --and I don't see anything going on in the log! =)
I guess it could be distracting, or not, depending on how 'animated' the animation is.. I would think the icon changing color, or displaying a badge wouldn't be all that distracting. A user could then mouse over it to see what Hazel is doing, or click view log to get further info.
My main use for Hazel is on my HTPC setup... I don't want it Growling all over the place if not necessary. But it would be nice to be able to enable a feature such as I suggested when I'm working on new rules/testing instead of having to go in and edit rules to make them temporarily notify me they're working.