Can a Jehovah's Witness say that they know they have eternal life?

Not even Jehovah's Witnesses who feel assured of having the anointing (in-dwelling) of the Holy Spirit as per Romans 8:9-17 can say they know they have eternal life - not according to Watchtower Society teaching on the matter, that is. With regard to your supplementary question, "Does this mean that an "anointed" can at least know that they have secured a place of eternal life on earth?" again the answer is "No."

I will deal with the supplementary question first as this will give insight into how radically different Watchtower Society teaching is on the entire matter of anointed Christians having a place either in heaven or on earth. Until the matter of how JWs view the whole "anointing process" is grasped, confusion will remain as to the main issue you raised.

The heavenly calling is said to be given to no more than 144,000 humans, and after they have faithfully completed their earthly lives, then at the point of death, they are assured of being in heavenly glory eternally. Only at the point of death are they assured of being in heavenly glory eternally. JWs believe that it is only the heavenly group who will ever be declared righteous, which is why the earthly group can never be totally certain that God views them as righteous. Let me quote from this Watchtower magazine:

"Before his death, Jesus introduced to prospective Jewish members of that new nation [spiritual Israel] the new covenant, which would be validated by his own blood. On the basis of their faith in that validating sacrifice, those taken into that covenant would be made 'perfect perpetually.' (Hebrews 10:14-18) They could be 'declared righteous' and their sins forgiven. (1 Cor 6:11)... They give up their earthly prospects in order to have an 'inheritance reserved for them in the heavens.' ...Likely, the full number of spiritual Israel, that 'little flock' of Kingdom heirs, has been selected." [Emphasis mine] Watchtower 1 September 2000, p22 para 15

But none of that applies to 99 per cent of JWs. Bear that in mind. It is crucially important to understand.

Further, the JW “Insight on the Scriptures” Vol. II, page 362 has the heading ‘Those for Whom Christ is Mediator’. After quoting 1 Timothy 2:5-6, it says Jesus

“mediates the new covenant between God and those taken into the new covenant, the congregation of spiritual Israel. (Heb 8:10-13; 12:24; Eph 5:25-27) Christ became Mediator in order that the ones called ‘might receive the promise of the everlasting inheritance’ (Heb 9:15); he assists, not the angels, but ‘Abraham’s seed’. (Heb 2:16) He assists those who are to be brought into the new covenant to be ‘adopted’ into Jehovah’s household of spiritual sons; these eventually will be in heaven as Christ’s brothers, becoming a part with him of the seed of Abraham. (Ro 8:15-17)”

"Holding the offices of Mediator and High Priest, Jesus Christ, being immortal, is always alive to plead for those of spiritual Israel [the 144,000 alone] approaching God through him, so that he can mediate the new covenant until those persons receiving his mediatorial assistance are saved completely. He is able to conduct matters to the successful completion of the new covenant. Those in the covenant are eventually installed in the heavenly priesthood as underpriests with Christ, their great High Priest." [Emphasis mine]

This means that JWs believe the 144,000 still need Jesus to mediate for them until they are eventually saved completely. That is why none of the 13,000 or so anointed JWs today can say they KNOW they HAVE eternal life. They can only believe that they have been saved partially, and that getting saved completely depends on what they do. And, given that they believe "They give up their earthly prospects in order to have an inheritance reserved for them in the heavens", they believe that becoming unfaithful will result in annihilation, as they no longer have an earthly inheritance - they apparently "gave up that right" in order to join the elite 144,000 class. (See Watchtower 15 August 2006 p31 where Adam and Eve's deaths are said to have resulted in their annihilation.)

This means that no JW can say that they know they have eternal life, for those without the anointing of the Holy Spirit do not have Jesus as their Mediator (he mediates only for the 144,00 according to the Society quote above) and even those who do may become unfaithful before they die and then face annihilation.

Summary Conclusion: The question said, "I have read some material indicating that JW may be certain that they have been "anointed"; but a provisional anointing gives no certainty at all, given that the person has to keep doing all the right things till the day he or she dies. There is only a hope that they might eventually 'make it' to heaven, so they have no assurance of salvation (to eternal life in heaven). This applies equally to JWs not having this provisional anointing, for they likewise have to keep doing all the right things till either their time of death or, if living through Armageddon, for a further 1,000 years on earth. They have the hope of salvation (to eternal life on earth), but - likewise - no assurance.

Jehovah’s Witnesses do not believe ‘Once Saved Always Saved’ is taught in the Bible.

Instead powerful promises like the words in John assure us that God will surely reward those who endure to the end. He will never fickly renege on his promise when a faithful anointed one endures to their death.

So John’s words that those who believe can know they have eternal life should be juxtaposed with those who do not believe. It is only those who believe that will be saved but belief is the first step in our walk with God. The Christian must continue that walk until the end to gain the reward.

Most of your question focuses on an anointed Christian brother or sister. As your question makes clear the individual who is spirit anointed has been given a token as it were, a special operation of the Holy Spirit, that serves as a pledge or guarantee of what is to come.

After you believed, you were sealed by means of him with the promised holy spirit, which is a token in advance of our inheritance.” (Eph. 1:13, 14)

Paragraph 7 of the Watchtower you cite asks:

Does the individual who is thus anointed have a guaranteed future in heaven?

The answer is no. While sure of their invitation, whether they finally receive their reward in heaven will depend on their proving faithful to this calling.

Therefore, brothers, be all the more diligent to make your calling and choosing sure for yourselves, for if you keep on doing these things, you will by no means ever fail. In fact, in this way you will be richly granted entrance into the everlasting Kingdom of our Lord and Savior Jesus Christ.” (2 Pet. 1:10, 11)

An anointed Christian must continue to remain faithful. Otherwise his heavenly calling, or invitation, will be of no value to him. — Heb. 3:1; Rev. 2:10.

As with all promises from Jehovah we don’t have to worry about Him holding up His end of the deal. We do have to concern ourselves with maintaining our standing with Him in such a way that we don’t void the guarantee.

If an anointed person turns aside from a faithful course they don’t then qualify for a “runner up”reward of earthly eternal life.

It’s not as if a Christian with a heavenly calling has to hit a longer tee shot than a fellow Christian with an earthly hope.
Both are called upon to maintain a course of integrity during their lives.

None of us can claim that eternal life is ours, only that we believe it is promised to us if we are faithful to the end.

Consider the words found in Philippians 3:12-16. (ESV)

12 Not that I have already obtained this or am already perfect, but I press on to make it my own, because Christ Jesus has made me his own. 13 Brothers, I do not consider that I have made it my own. But one thing I do: forgetting what lies behind and straining forward to what lies ahead, 14 I press on toward the goal for the prize of the upward call of God in Christ Jesus. 15 Let those of us who are mature think this way, and if in anything you think otherwise, God will reveal that also to you. 16 Only let us hold true to what we have attained.

Additional info is found in this article.