My thought would be no for the following reasons:
1. The bumper is not plastic but polyurethane or fiberglass mix if aftermarket
2. Your bumper is painted and followed up with clear-coat
But hey it might work since it is a mild abrasive cleaner, but I would think you would want to use a polish or rubbing compound designed for clear-coat and try to buff it out.
just my .02, not an expert on the matter by far
Here is a link that may be of help.
http://www.paintcare-n-detailing.com/