I don't think there is any reason to draw any connection at all other than coincidence. If I told you I had four eggs for breakfast this morning and then later told you that at four my sister was coming over for a visit would you try to draw some meaningful connection?
Paul talked about his pending visit back in 12:14-15 as well. Each of his trips were accompanied by a different situation. The first one was the original church plant. We hear from chapter two that his second visit was painful. For his third trip he's set out his intention not to be a burden while there.
However his coming was a warning. He knew there were problems in the church and that they needed to be dealt with. In some senses he is calling them to get their act together before he gets there. In chapter 13 he reminds them that he's coming again, then gives them an outline of some of the things they need to work on.
Remember the grammatical layout of our Bibles is contrived as best the translators were able to because the Greek doesn't have the same punctuation or formatting that we use. You could easily use the first bit of verse 1 as a subject heading, then start the paragraph with the second phrase.
In short, there is no particular connection to this being his third visit and the fact that charges against a sinning brother should be established by two or three witnesses. True his presence might have contributed one more witness (presumably there was one there already aware of the issues and reporting them to Paul) but there is not some magical numerical significance here.
I was trying to draw some link...
Be careful about trying to draw links where the text doesn't actually indicate them. You can make a lot of wacky mistakes in understanding the Bible if you set out trying to find connections that aren't specified.