Does Photos get confused when tagging a person whose face is not visible? I want to tag the people in my photos, even if their faces are not visible. Does this confuse the facial recognition function and reduce the success rate? Is there another way to tag people?
In a sense, yes.  Photos uses facial recognition algorithms that improve their accuracy through acquiring more data with which to reliably match a person’s face.  This is why you are asked to mark wrong matches as well as correct ones, as this all helps the software produce more reliable results.

Tagging a person with no face will feed false data to the algorithm, which will then believe it should start searching for faces that look more like an elbow, or something.

The application itself during the earlier stages of tagging alerts you with a recommendation only to tag faces that are clear, and to avoid even blurry, out-of-focus faces, or faces that are turned to the side.

I, personally, ignore those two particular rules, and at the end, it is your decision how you choose to tag photos.  There’s nothing inherently wrong with doing what you’re doing if you’re content to match more photos manually than relying on the facial recognition engine to do it for you.

Addendum: One idea I can think of as an alternative means to tag people in photos without compromising the facial recognition effectiveness would be to use keywords, i.e. to create one keyword per person comprising a first and last name.  This will have the benefit of making the photos searchable by a person’s name in a similar fashion to searching for a face.