Chances are that whatever helps you excel at the Putnam will also show in other parts of your application, particularly your coursework, your letters of recommendation and your math subject GRE score. In that sense the Putnam score won't "add" anything: it's just another reflection of your strengths.
On a more logistical note, I imagine it's tricky to mention that range Putnam score on an application in such a way that it won't raise an eyebrow. (Scores in the Honorable Mention range could be listed in the "awards" section.) If I were you, I would probably not mention it myself and trust that my professors mention it in their letters of recommendation if they deem it relevant.
If you do want to mention your Putnam accomplishments yourself, give your ranking rather than your score. Scores are pretty meaningless because the difficulty of the exam varies so much by year. Last year a score of 20 was barely enough to get into the top 1,000. In difficult years, a score of 20 can get you into the top 200.