Well, given the parameters of his worldview, maybe. But It seems to me that he's perfectly willing to adjust his deeply held strict constructivism in order to accomodate his desire to foist his religious and moral perspectives on the country. Here's what Hilzoy at Obsidian Wings has to say:
Scalia argues that displaying the Ten Commandments does not favor one religion over another in this way. Here is his argument: He says that "the principle that the government cannot favor one religion over another" is "a valid principle where public aid or assistance to religion is concerned". However:
"it necessarily applies in a more limited sense to public acknowledgment of the Creator. If religion in the public forum had to be entirely nondenominational, there could be no religion in the public forum at all. One cannot say the word "God," or "the Almighty," one cannot offer public supplication or thanksgiving, without contradicting the beliefs of some people that there are many gods, or that God or the gods pay no attention to human affairs. With respect to public acknowledgment of religious belief, it is entirely clear from our Nation’s historical practices that the Establishment Clause permits this disregard of polytheists and believers in unconcerned deities, just as it permits the disregard of devout atheists. (...)
Historical practices thus demonstrate that there is a distance between the acknowledgment of a single Creator and the establishment of a religion. The former is, as Marsh v. Chambers put it, "a tolerable acknowledgment of beliefs widely held among the people of this country." Id., at 792. The three most popular religions in the United States, Christianity, Judaism, and Islam—which combined account for 97.7% of all believers—are monotheistic. See U. S. Dept. of Commerce, Bureau of Census, Statistical Abstract of the United States: 2004–2005, p. 55 (124th ed. 2004) (Table No. 67). All of them, moreover (Islam included), believe that the Ten Commandments were given by God to Moses, and are divine prescriptions for a virtuous life. See 13 Encyclopedia of Religion 9074 (2d ed. 2005); The Qur’an 104 (M. Haleem trans. 2004). Publicly honoring the Ten Commandments is thus indistinguishable, insofar as discriminating against other religions is concerned, from publicly honoring God. Both practices are recognized across such a broad and diverse range of the population—from Christians to Muslims—that they cannot be reasonably understood as a government endorsement of a particular religious viewpoint."
Or, in my summary:
(1) The framers, and others since then, did invoke and acknowledge God, so invoking and acknowledging God must be consistent with the establishment clause as they understood it.
(2) But invoking and acknowledging God necessarily favors monotheism over polytheism or atheism, where monotheism is understood as the view that there is one God who pays attention to human affairs.
(3) So any acknowledgment of religion that merely favors monotheism, so understood, over other religious views is OK.
(4) The three most popular religions in the US are monotheistic, and all of them acknowledge the Ten Commandments as sacred.
(5) So displaying the Ten Commandments does not favor one version of monotheism over others; it simply favors the major variants of monotheism over atheism and polytheism. It thus does not endorse a particular religion, and it is therefore OK on the same grounds as invoking God.
Here's what I've never understood about Scalia: Does he even understand why we have a Bill of Rights? Now, granted, I was first told this in my high school civics class, so perhaps Scalia missed it from his lofty perch on the Supreme Court, but I was always told that the Bill of Rights exists to protect minority rights. Scalia is really not a strict constructionist, but is actually a majoritarian: He is willing to bend constitutional protections of minorities in order to accomodate the majority (thus turning the Bill of Rights on its head).
But that's not really right either. He's not really a strict constructionist or a majoritarian, since when it's convenient he's happy to support the minority over the majority (Bush v. Gore, anyone?). Scalia's a brilliant guy. He's so brilliant that he's able to subtly shift from position to position on the philosophical map while claiming to hold a consistent position. As long as he defines what he's doing as strict constructionism, it doesn't really matter whether what he argues is actually a strict construction. He simply doesn't care about the consistency of the grounds of his arguments. He's a brazen opportunist who changes positions to support whatevery he thinks the constitution should say rather than what it does say. (This would probably qualify as bullshit in the strictly philosophical sense.)
Wait, isn't this what conservatives always accuse judges of doing when the disagree with their decisions? I guess opportunism is contagious.