Perhaps...
But consider this. The Hebrews had a great deal of history behind the Christianity. In the past documents inspired by God's prophets have always been added to the library of the synagoge and look to what lengths the Hebrew and Greek scriptures were preserved to assure there existence to future generations. Perhpas it's not so reasonalbe to assume that that Paul didn't realize that these..."personal" letters would be added to canon.
I do consider it but find more problems with it than what we started with. Paul, while he believed he was a messenger of God sent on a mission, obviously did not count himself among the prophets of old. It seems to me that Paul suffered from a self-esteem problem; if you look at his letters in chronological order, you see his introductions of himself getting more and more harsh and self-demoralizing. Here is a sequence pulled from scriptures:
"I, Paul, an apostle—sent not from men nor by man, but by Jesus Christ and God the Father" (Galatians)-->"I am not at all inferior to the most eminent apostles" (2 Corinthians 11:5) -->"To me, who am less than the least of all saints" (Ephesians)-->Paul and Timothy, servants of Christ Jesus"" (Philippians)-->"Paul, a prisoner of Christ Jesus" (Philemon).
My opinion would be that Paul had a self-confidence problem that he never got over, but regardless of that, it is clear enough from this that he most likely would have reservations as to his letters becoming canonical, especially towards the end of his writing career. Your passage was from 2 Timothy, which was actually Paul's
last letter, which puts it in the major thickness of the seething disgust through which Paul saw himself. (This is speaking nothing of his tangential rants on how unworthy he is because he once persecuted the church...seems like he never forgave himself for that one.) If you would like another passage pulled from scripture to give you a context of Paul's self-image while writing these latter letters, here is one from 1 Timothy, which self-evidently directly preceded 2 Timothy: "This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners; of whom I am chief." (1 Timothy 1:15 KJV)
There is another point to be made that suggests my earlier presumption (that Paul did not intend his letters to be canonical) is the case. Take a look at Philemon 3:12-13. It says this:
"As soon as I send Artemas or Tychicus to you, do your best to come to me at Nicopolis, because I have decided to winter there. Do everything you can to help Zenas the lawyer and Apollos on their way and see that they have everything they need."
From that passage alone (and there are several like this, I picked this particular one because it happened to be on the page I glanced down at), does it seem like Paul was thinking that this personal letter would one day be included as part of the infallible, unmitigated, and eternal truth of God; one that applies across all subsequent generations? Today, are we to expect visits from Artemas and Tychicus, and then go to Nicopolis to meet Paul (because he would apparently still be there "wintering" if this is part of eternal God-truth). Are we to look for lawyer Zenas and Apollos so that we may do everything to help them have everything they need?
I hope you catch my flippant tone and recognize the absurdity of these questions. The answers are obviously "no". Those words weren't meant to exist for any other time but for then and there. They are certainly not what you would expect as eternal truth-words, but absolutely what you would expect if a man was writing a personal letter to his friends, with his personal opinions attached.
So even by your own source, the potentiality that Paul WAS expecting his words to be in the biblical canon is highly unlikely (unless we are to assume that Paul deliberately and manipulatively wrote passages like these to throw us off, simultaneously wanting this to be a subject of uncertainty and controversy, which would bring a whole new slew of questions to the table concerning whether or not a man who would wish this upon subsequent generations should be given the authority of Godword.)
In short, no, your hypothesis IS unreasonable.