Well I just actually did the opposite, had highlights put in my hair...and I was shocked to find that my circles look worse now that my hair is lighter. Why? because there is more of a color contrast. As long as you don't choose too ashy a brown tone..you'll be fine(any gray or ash tone will accentuate it), warmer tones are the way to go. If anything it will look better.
However, instead of trying a box color(esp not one that only lasts a few shampoos, you'd have better results getting those streaking wands that were popular many years ago)...you're best bet is to get yourself into a salon. The process ( a semi permanent) will be custom blended for the right tone. Box colors over blonde tend to over-darken hair. For between $20-$50 more, you're getting a guarantee that it will suit you. Not only that, but putting a color over a lighter color means that you are going to want your ends trimmed right away. Any split ends(or just plain ol dead ends) you have may not take the color. Trust me, it's worth it.