The answer, in my view, is both entirely yes and not really at the same time. Here's why:

The United States of the nineteenth century was an overwhelmingly religious country. Even compared to today's US, which is much more religious than most of Europe, people believed during the nineteenth century. In particular, they believed that America was a moral exemplar to the rest of the world. The Puritan leader John Winthrop famously coined the description of America as "a city on a hill," meaning an example of a society that would model proper morality, which meant religion, for the rest of the world, much of which was mired in hopeless sin and depravity. Now, the America of 1845 (the year of the coining, or at least popularization, of the phrase "Manifest Destiny"), was very different in many ways from the America of 1620. The history of the development of the religion of the Puritans into the religious and philosophical movements of the early nineteenth century are interesting in their own right, but perhaps a bit extraneous. What matters is that Americans still saw themselves as the "city on the hill," the exemplar of virtue. This exemplary status was derived from God, and it required Americans to spread their own exemplary culture around the world, enlightening others to be the same as the perfect society they had created.

And yet, you could also say that this was not the case. For while Americans of the time were much more devout on a day-to-day basis than we are used to today, they were by and large not religious zealots in the same way that the Puritans were. The country also by the 1840s began to absorb large numbers of European Catholics via immigration from Ireland, Germany, and other countries, somewhat limiting the effects of Protestant dominance. Manifest Destiny was (is) an ideology, and ideologies have a slippery way of purporting to be about one thing, but rather being about something else. For one thing, many proponents of Manifest Destiny were Southern slaveholders, who sought to increase the number of slave (or slavery-friendly) states in order to ensure the continued survival of the "peculiar institution" in the face of mounting Northern censure. Some of these people--and others--were also motivated by a racist belief in the inferiority of Indian, Hispanic, and other non-Anglo peoples. They saw the triumph of the white race as natural and inevitable. Other supporters of Manifest Destiny, whatever their racial views, were naked capitalists, who sought to leverage the natural resources of the continent to their own personal advantage. They may or may not have been personally racist, but they were personally ready to expand the United States for financial gain.

To summarize: as an ideology, Manifest Destiny was undoubtedly descended from a religious ideal of a virtuous, exemplary society. But it was also flexible enough to accommodate supporters for whom religion was not a terribly important aspect of life, and who supported the expansion of the American state for other, mostly non-religious reasons.

Sources:

Weeks, William. Building the Continental Empire

May, Robert E. Manifest Destiny's Underworld

And finally, I recommend as I always do, Daniel Walker Howe's What Hath God Wrought as the premier synthetic account of American history before the Civil War. The chapters near the end of the book on westward expansion and the Mexican War, will present a useful summary.