Part of Francis Bacon's original hopes for his new science was that, given enough data, some knowlege might be gained of the patterns of God's providential working, as well as the regularities of nature.
You'll see the catch in that - he assumed that one would first be able to distinguish the "natural" from the "providential", thus showing how he worked from a different worldview than the methodological naturalist who would start by subsuming such "patterned" providences into nature.
If we took Bacon's line regarding healing miracles, then "theistic" science could certainly be done. Craig Keener documents sources from around the world for thousands of healings, acknowledging that the quality of reprts varies widely (for example, the difference between the publicity of a Televangelist and what he witnessed himself).
But it would be quite possible, if one avoided hypercriticism, to do statistical analyses for the kinds of healings claimed amongst various conditions, geographical or denominational variations, and so on. It would start as sociological work, because it necessarily depends on human reports, and would therefore inevitably give results more like sociology than physics, even before one got to trying to discern patterns of divine activity rather than human activity (eg if Africans are healed more, it may well be because they pray more - obvioulsy trelavant if the study is about "answered prayers").
So it's quite possible, but fraught with the hazards of any sociological research - the main one being that neither the objects of research nor researchers can be free of bias.