Can you add housing by working tiles more than 3 tiles from your city center?

In Civ 6, cities require housing, and one source is from tile improvements (0.5 per improvement): Farms, Fishing Boats, Pastures, Plantations, Camps.

As in Civ 5, citizens can only work tiles within 3 tiles of the city center. However, eventually the national borders will expand further than that. I am wondering if you can add improvements to those tiles to further boost housing.

There would be some precedent for that, since you can obtain luxury resources in this way. I was able to create a plantation to harvest tea in a tile 4 tiles away from my city center, even though I can't work it.

The answer in short is yes you can. Resources of any kind, housing additions and such all get added to your empire and nearest city when you obtain them, just as you said yourself.

since you can obtain luxury resources in this way. I was able to create a plantation to harvest tea in a tile 4 tiles away from my city center, even though I can't work it.

The thing that you obviously do not get is the yield since you are not actually working the tile, also like you said.

Housing additions such as the 0.5 from farms etc, also applies to neighborhoods. Those are not required to be worked and can be built outside the 3 tile working range.