No. it does not..
it says if THEY (the people the whole chapter is talking about) fall back again (leave the presence of the church, and the good things that even a non believer can gain from it)
it goes right along with 1 john,, where it talks about people who were in the church, and left and are now against christ. they were NEVER OF US (saved) for if they were TRULY OF US (saved) they never would have departed.
Eternally-grateful is willfully blind. First of all the main disagreement with eternal security is torn apart in this 'letter' (there were no chapters originally it is referring constantly to the beginning). The main heresy is that we can sin & still be saved, which is what Calvinism teaches, hence they came up with eternal security. I recall Billy Graham saying that Johnny Cash who never overcame his bad drug habit (because he never knew the truth that it would land you in hell) was free in heaven. Whereas the bible plainly states that a 'drunkard' or a 'glutton' will not inherit the Kingdom of God, can we not safely include the drug addict ?
How about Greg Laurie talking about his mother. He was surprised & relieved to learn that she had made a confession of faith in Jesus & thought of herself as a christian. The surprise was because she had many different abusive men in her home, she was always intoxicated & neglectful. Yet he says, you see, you never can tell by the way a person lives what is in their heart. Again the bible declares the opposite, we can tell what is in your heart by exactly that, how you live. Eternal Security is a silly man made doctrine which was never heard of before John Calvin, a vile sinner to the end. This passage describes him completely since you say it speaks of false teachers being entangled in sin themselves.
To directly answer the comment, which is ridiculous, this scripture is continuing the thought of the beginning of the letter:
2Pe 1:2 May grace and peace be yours in full measure through your knowledge of God and of Jesus our Lord.
2Pe 1:3 God's divine power has given us everything we need to live a truly religious life through our knowledge of the one who called us to share in his own glory and goodness.
2Pe 1:4 In this way he has given us the very great and precious gifts he promised, so that by means of these gifts you may escape from the destructive lust that is in the world, and may come to share the divine nature.
2Pe 1:5 For this very reason do your best to add goodness to your faith; to your goodness add knowledge;
2Pe 1:6 to your knowledge add self-control; to your self-control add endurance; to your endurance add godliness;
2Pe 1:7 to your godliness add Christian affection; and to your Christian affection add love.
2Pe 1:8 These are the qualities you need, and if you have them in abundance, they will make you active and effective in your knowledge of our Lord Jesus Christ.
2Pe 1:9 But if you do not have them, you are so shortsighted that you cannot see and have forgotten that you have been purified from your past sins.
2Pe 1:10 So then, my friends,
try even harder to make God's call and his choice of you a permanent experience; if you do so,
you will never abandon your faith.
2Pe 1:11 In this way you will be given the full right to enter the eternal Kingdom of our Lord and Savior Jesus Christ.
We do not escape sin by going to church !! We escape sin by an experiential knowledge of Jesus Christ. That is what the word epignósis means. It is the 'knowledge of our
Lord', they made Him Lord & did not do what Peter advises in the beginning of the letter to constantly build & grow in the faith so they did what he is warning against - abandoned the faith, whiles still claiming to be a christian, like Johnny Cash.