The source of the Ramban is the Sifra. The Torah says, "And I will lay the land desolate, and your enemies who live in it will find it desolate” The Sifra says: “This is a kindly measure, so that Israel should not say, ‘Since we have gone into exile from our land, now the enemies are coming and finding satisfaction on it.’ Therefore it says ‘And your enemies who live in it will find it desolate’ – even the enemies who come afterwards will not find satisfaction in it.” From the Sifra it sounds as though the kindness is that if we can’t use our land, at least it gives us some comfort that no one else can use it either. But it seems strange that the Torah would endorse such a selfish attitude - the attitude of the wicked Sodomites (Bava Basra 12b).

But the Ramban (on v. 16) explains more: “This is a good prophecy, foretelling that during every exile, our land will not accept our enemies. And this as well is a great proof and promise to us, since you will not find in all the inhabited world a land that is so good and accommodating, and that was once settled, that is now as destroyed as it [the Holy Land] is. For since we left it, it has not accepted any nation or language; all of them are trying to settle it but cannot.”

These words of the Ramban are often quoted by Zionists as a proof that their state is the long-awaited redemption. The land miraculously did not accept any other nation, and now it is accepting the Zionists with open arms, they say. Usually they quote this in conjunction with the Gemara in Sanhedrin 98a, which says that Eretz Yisroel producing fruit is a signal of the beginning of redemption. The problem is that the Gemara refers to the land miraculously producing new fruit every day (Maharsha). Regular fruit is not a sign of anything, and indeed the land produced regular fruit throughout the centuries of exile. We see that the Kesef Mishneh (Hilchos Terumos 1:11) tells the story of a practical dispute among the rabbis of his time over the issue of taking maaser from produce grown on gentile-owned land in Eretz Yisroel.

The Ramban as well never says that the land will not produce fruit when gentile nations plant it. He says that they will not be able to settle it, meaning that no nation will live long there before they are conquered, killed and expelled. A quick look at the historical record shows us what the Ramban means. The Holy Land was conquered by the Romans, the Persians, the Byzantines, and then the Muslims. For over a thousand years following the Muslim conquest, the land underwent a series of devastating invasions, followed by massacres of the existing population. Seljuk Turks and Fatimids were followed by Crusaders, who were followed by waves of Mongol tribes, who were followed in turn by Tartars, Mamluks, Turks and continual Bedouin raiders.

In this history of a land plagued by incessant wars and conquests, Zionist history is no exception. In a mere 61 years, the Zionists have fought eight wars and confronted two prolonged uprisings. Just as the troubles encountered by the gentile nations who tried to settle the land were a fulfillment of v. 32 “and your enemies will find it desolate,” so too the troubles encountered by the Zionists are a fulfillment of v. 33 “and I will draw out a sword after you,” as the Ohr Hachaim explains – that these words refer to the punishment for violating the oaths.

The Ramban explains that the “kindness to Israel” mentioned in the Sifra is that it is “a great proof and promise to us” i.e. a proof that G-d has not abandoned us and will still keep His promise to redeem us. Now we can understand the connection between v. 32 and v. 33. In v. 33 G-d warned the Jewish people with an oath not to return to Eretz Yisroel before the proper time (And I will scatter you among the nations, and I will draw out a sword after you; and your land will be desolate, and your cities waste - see Ohr Hachaim who connected this with the Three Oaths). But He knew that there would be some Jews who would think He had abandoned them in exile, and they would feel they had no choice but to take the initiative and redeem themselves by force. Therefore He prefaced the oaths with the promise that the gentile nations will never be able to settle the land permanently. The fulfillment of this promise will serve as our sign that G-d is still with us and we must keep the oaths, and wait patiently for the time when He sees fit to redeem us.

Regarding your second question whether the state has any connection with moshiach, the answer is that it may, we don't know Hashem's plans, but that should not concern us. As the Brisker Rav put it, "The Rambam writes that we can see the hand of Hashem even in the spreading of the major religions of the gentiles. These religions serve to prepare the world for the Days of Moshiach, by bringing belief in Hashem and the Torah albeit in a corrupted form - to the whole world. Does that mean that we should go and help spread these religions?" (Teshuvos Vehanhagos v. 2, siman 140)