Yes, and it should be recalled that the bitter religious wars which had roiled England (as well as much of Europe) was too recent in memory not to have its effect on their thinking. In fact, in America its effects lasted well into the Twentieth Century.
Indeed, this is so important to remember when trying to evaluate the religious ideas of the Framers, and the form they took in the drafting of the Constitution.
There's an interesting tension in the thought of both TJ and Adams WRT God and religion. On the one hand, God is the source of individual liberty; on the other, religion can be a grave threat to individual liberty (e.g., the Roman Church in their view). Not to mention that, historically, religion has often enough been the pretext for going to war; on the other hand, the best defense against tyranny is to vest the sovereignty of the state in The People (as the Framers did). But this only works on the understanding that The People are a people "under God."
In short, for TJ and Adams both, true human liberty is achieved only "under God"; where God is absent, the tyrant will fill His place.
YHAOS, thank you again for the link to the TJ archive. I breezed through it just to see what-all was there. Truly, it is the "mother lode" of TJ's writings over a lifetime. A wonderful resource!