I've touched on this when discussing Thomas Madden, one of the few historians who puts this view forward. In short, no, but the papacy did their best to make it seem that way.

It's hard to really ascribe any particular intention to the Crusades, not the least because they weren't even all against Muslims or in the Middle East! Similarly, we can't really say the intentions of any given Crusader, except of course those for whom there are proper accounts of their reasoning for going. Similarly, it wasn't necessarily one unified army with the Pope commanding, so while a mostly united force, the head of each force may have had different reasons.

I'll go with the First Crusade, since it was the one that kicked it off. This site preserves several contemporary-ish (within a few decades, as far as I'm aware no chroniclers were furiously scribbling in real-time as he spoke) accounts of Urban II's call to arms from individuals present. IMPORTANT: These are accounts of what the Pope said. There is much research done on other long-standing, complex social/cultural/political/etc. reasonings behind the Crusades, these are just some contemporary accounts.

Being absolved of sins is a point that comes up over and again. That it's a holy cause, and "All who die by the way, whether by land or by sea, or in battle against the pagans, shall have immediate remission of sins" and "Let those who for a long time, have been robbers, now become knights." This alone would likely have been cause enough for many but, again, I don't want to necessarily infer intentions of individuals.

The defense of the Byzantine Empire (variously referred to as Greeks, Eastern Church, etc.) comes up again and again as well, of course. Sometimes there's an aspect of retaliation, such as calling "promptly to those Christians and to destroy that vile race from the lands" and describing terrible acts of violence and torture, or referring to Muslims as worshipping demons (note that that's what the chroniclers recounted Urban as saying, but does not necessarily mean it occurred, nor am I saying they never did, but propoganda is not only a modern thing). Other times it seems to be more generally religious and political, that the Byzantines are Christians and are losing their Christian territory and Christian subjects/sites, which is bad, so they must be driven out as a kind of offensive defense: "They have occupied more and more of the lands of those Christians, and have overcome them in seven battles. They have killed and captured many, and have destroyed the churches and devastated the empire. If you permit them to continue thus for awhile with impurity, the faithful of God will be much more widely attacked by them."

Reclaiming holy sites also comes up frequently, as does ensuring the safety of pilgrims, but it's important to note that Jerusalem had been Muslim-controlled for centuries at that point, not that they were looking to reclaim something recently lost.

Guibert de Nogent also indicates that it is necessary for defending against the coming of the Antichrist: "For it is clear that Antichrist is to do battle not with the Jews, not with the Gentiles; but, according to the etymology of his name, He will attack Christians. And if Antichrist finds there no Christians (just as at present when scarcely any dwell there), no one will be there to oppose him, or whom he may rightly overcome."

The most interesting to me is Robert the Monk citing overpopulation as a significant problem in Europe, and that taking the Holy Land would give them more space and alleviate the issues: "since this land which you inhabit, shut in on all sides by the seas and surrounded by the mountain peaks, is too narrow for your large population; nor does it abound in wealth; and it furnishes scarcely food enough for its cultivators. Hence it is that you murder one another, that you wage war, and that frequently you perish by mutual wounds. Let therefore hatred depart from among you, let your quarrels end, let wars cease, and let all dissensions and controversies slumber. Enter upon the road to the Holy Sepulchre; wrest that land from the wicked race, and subject it to yourselves."