If the groundwater has a short path (and residence time) to the artesian well outlet, then I think it could have a little oxygen.

If it goes through some caverns and the water drips through air-filled spaces, then I think it could have a little oxygen.

If it goes through a typical bedrock or alluvial aquifer, then it probably has fairly low oxygen. Generally there are some oxidation reactions with some of the minerals and that use up the available oxygen.

One exception might be if there are lots of plant roots (trees and deep-rooted grasses) that reach into the aquifer. During active plant growth periods, the roots can supply a little bit of oxygen to the soil and the aquifer. However, the converse is true after the first hard freeze. After the plants become dormant, any decaying organic matter in that type of aquifer will consume the available oxygen.

Is that enough of an "it depends" answer for you?

I would wildly speculate that if his pond level is still rising for a few days after a rain, then the groundwater may be on a short path and may still contain some oxygen. Otherwise, I would expect that water is fairly low oxygen.

P.S. If the topography is just right, then he could build a spring box upslope to capture some of the water flow. Then use some pipe to bring it part way down the slope. If it has enough head, then he could build a splash pad and rocky waterfall to add some oxygen before the water enters the pond. Could make an attractive water feature and be cheaper than adding aeration. (However, that would be far less effective than a nice bubbler aeration system.)