The language on the Free Trial is not clear. It could be interpreted that the free trial will be canceled, but there might be charges that won't be refunded. If one cancels by the date required by Dropbox, is there a guarantee that NO CHARGES will appear on my card?
Provided that you cancel the trial by the date shown on the website, then there won't be any charges to the plan.
Bear in mind that trial expiry is also time specific, so activating a trial at 1pm on one day, using the trial, and then cancelling on the expiry date at 2pm would be considered outside the trial period, so then you would be charged. Make sure to cancel before 1pm in that instance.