In the Times online the author David Selbourne answers this question "No," and gives 10 reasons why not. Some of his points echo those A Waco Farmer and I have made at different times, though we have not descended into Spenglerian gloom yet.

Read the full article. In brief, his 10 points are (quoting the first sentence of each paragraph):

1) The first is the extent of political division in the non-Muslim world about what is afoot.
2) The second reason why, as things stand, Islam will not be defeated is that the strengths of the world community of Muslims are being underestimated, and the nature of Islam misunderstood.
3) Indeed, the third reason why Islam will not be defeated, as things stand, is the low level of Western leadership, in particular in the United States.
4) Next is the contribution to the disarray of Western policy-making being made by the egotistical competitiveness, and in some cases hysterics, of “experts” and commentators on Islam.
5) The fifth disablement is to be found in the confusion of “progressives” about the Islamic advance.
6) The sixth reason for Islam’s growing strength is the vicarious satisfaction felt by many non-Muslims at America’s reverses.
7) The seventh reason lies in the moral poverty of the West’s, and especially America’s, own value system.
8) The next indication that Islam’s advance will continue lies in the skilful use being made of the media and of the world wide web in the service both of the “electronic jihad” and the bamboozling of Western opinion by Muslim spokesmen.
9) The ninth factor guaranteeing Islam’s onward march is the West’s dependency on the material resources of Arab and Muslim countries.
10) Finally, the West is convinced that its notions of technology-driven modernity and market-driven prog- ress are innately superior to the ideals of “backward” Islam.

Hat tip Jihadwatch.