Guess it depends on who is reading it on how it's interpreted.
Do you think background information regarding the individuals, the discussions, the discourse regarding natural religion that is occurring in the Colonies, in Britain, and on the Continent at the time is important to that interpretation?
If not, then sure, interpret it however you want (i.e., simply make the interpretation align with your preferred set of beliefs). If so, however, then you have to take into account what Franklin is writing, what Jefferson is writing, what Thomas Paine had written and his relationships with the individuals writing and signing the DoI; you must take into account Hume, Locke, Shaftsbury, Hobbes, Mandeville, Adam Smith and his Theory of Moral Sentiments, Butler, Hutcheson, etc.
Some of the signers of the DoI were devout Christians, hell, some were preachers. However, some were radical deists, to include the author of the DoI. So, you need to interpret in the light of what this group of individuals would have agreed to as a group, and agreed to unanimously. All 56 of them signed on and agreed with the DoI. Jefferson certainly is not agreeing to a rigorous concept of a Christian personal God. But, Jefferson would agree to a Creator. The devout Christians might have wanted stronger language, but they would agree to a Creator.
