I think cleansing would, by definition, cause you lose a lot of glycogen and along with it, a lot of water, which in itself might make you look less puffy. So sure, you'd probably look leaner.
As far as reducing inflammation, I'm not sure. If, by cleansing, you were eliminating some inflammatory foods or habits that were part of your lifestyle, then sure it would reduce inflammation. However, I suspect that cleansing itself might be inflammatory.