Question: Does the Greek text of 2 Tim. 1:16-18 imply that Onesiphorus had already been dead by the time of writing these words?:

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> The Lord give mercy unto the house of Onesiphorus; for he oft
>  refreshed me, and was not ashamed of my chain: But, when he was in
>  Rome, he sought me out very diligently, and found me. The Lord grant
>  unto him that he may find mercy of the Lord in that day: and in how
>  many things he ministered unto me at Ephesus, thou knowest very well.
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Answer: 
I think that we need to understand firstly that Paul is contrasting Onesiphorus and his household with those people he mentions in v14. He is commending them for their care of him. 

The fact that it is just Onesiphorus' household that Paul speaks of in v15 and not Onesiphorus himself suggests that he wasn't there at the time. That might mean that he was dead, or it could simply mean he was elsewhere, after all Paul refers to the household of Stephanas in 1 Cor 16:15 when he is very much alive (just not at home 1 Cor 16:17)

It is easy to read a lot into the term "The Lord grant mercy to" in v15 and conclude that Paul was praying for comfort for the household. But that is not what he says. Notice in v18 he also prays for mercy for Onesiphorus as well and it doesn't seem to me that praying for mercy for one already dead would fit with Paul's theology. Paul is always praying/ asking for mercy or grace for people. Many of his letters open with such a prayer: Rom 1:7, 1 Cor 1:3, 2 Cor 1:2, Gal 1:3, Eph 1:2, Phil 1:2, Col 1:2, 1 Thess 1:1, 2 Thess 1:2, 1 Tim 1:2, 2 Tim 1:2, Tit 1:4, Phm 1:3 

In the end the evidence is not conclusive either way, so it seems clear that Paul presumed Timothy would know the situation, and that beyond our own curiosity the question does not have a great significance. By that I mean that we should not build a doctrine upon this as a key text, or even use it as a proof text for 'prayer for the dead' etc. The ambiguity precludes it's worth to that end.
According to the current official teaching of the RCC, purgatory is not a place to PAY for one's venial sins, but a place of purification to prepare the deceased 'Christian' to live in heaven. Thus, purgatory implies that the person enduring it already has full pardon or mercy in Jesus. The person's sins are redeemed by Jesus' death on the cross. The person in purgatory is said to already be forgiven. The person is assured heaven in the official view and so we cannot conclude that 2 Timothy 1:16-18 is proof of purgatory. So is it then proof of hell then? We cannot conclude that either for the fact that mercy is assured to the one who has met the conditions of divine pardon in this life. If Onesimus was dead and Paul was praying for mercy, then it would imply Paul was praying that Onesimus would be able to avoid hell. And such an interpretation would also be speculation.