docbud is confused about the meaning of "improve". The question at hand is what does a Citadel connect to the trade network. The phrase "improves a resource" is something taken from the game's 'Pedia to refer to the connection of resources, yet "improving" also is used to speak of the use of "improvements" in many other ways. And improvements and resource connection are two different things. Thus, let me avoid using the term "improve" for a while.
There are a few legal improvements for any given tile, but at most one improvement may be used on it. When putting an improvement on a tile, the game preserves the "at most one" rule by immediately erasing any improvement there. This is easily seen by trying it out. It's harder to construct a scenario to see that the same happens to a pillaged improvement, but it's the same rule.
You can connect a strategic or luxury resource to the empire either by using a legal improvement on it, or by building a Feitoria in the City-State's territory. Feitorias have their own rules. When we exclude them, we see that improvements can only connect the resource they are sitting on, hence we can say they "improve" that resource, or fail to. Improvements are "legal" for connecting strategic and luxury resources under two conditions. One, the improvement must not be pillaged. Two, the improvement must be defined to improve that strategic or luxury resource.
When it is said that a Great Person Tile Improvement improves strategic resources, it means that putting a Citadel on Horses connects those horses to your empire. It doesn't put a Pasture on the tile, it just outright connects the Horses, because Citadels are defined to do that for Horses just as Pastures are.
When a Citadel is put on an Oil tile, the Oil should be connected. It's irrelevant what other improvement was on the tile, because that improvement is gone.
