I think that most people will answer the question in the title with 'yes', and, until recently, I was one of them. However, my wife, who is not a native English speaker, does not do this; and, when I was about to correct her, it occurred to me that in fact her approach is the more logical. After all, if it were all on one line, I would write "Dear recipient, this is a letter to you." and not "Dear recipient, This is a letter to you."; and I am unconvinced that the interpolation of a line break after the comma should change anything.
There being no governing body for English, inevitably the natural way to answer is "that's the way it's usually done, and logic can go hang", so let me ask a more precise version of this question: does any standard reference book require, forbid, or otherwise discuss this practice? I went Googling, but without luck.