Not if you use the Secure Messaging system on americanrexpress.com
My spouse used this method to cancel the card 6 months ago when her travel for business dwindled. It was simple and painless. However, in the past month there was a boost in her air adventures and she reapplies. Not only did she get instantly approved but received 25000 mr points. I told her she should have gotten a referral from a friendly fter in order to share the wealth.