The logical answer is, probably not.
However, being a COPD patient myself, I had several young, healthy pets before I got diagnosed with COPD and they are like my family
to me. Taking them from me now that I am having to deal with the stress of the disease, would only stress me more and make my symptoms worse, in my opinion. Sometimes, I have to ask a friend or relative to come in and help me with them, or take a run to the store for food, if I can't go. But, other than that I care for them myself. They give me company, comfort and the will to tolerate the bad days I have with the COPD. They don't judge me or tell me what I should or shouldn't be doing. They are there for me. They support me.
So in truth, pets? Just depends on the personal situation and how advanced the COPD is. If the person is bedridden or can't function on their own, then no. Pets would not be a good idea to be kept on a permanent basis, unless you have a live-in caretaker who is willing to look after a pet as well. On the other hand, if the person who has the COPD feels confident enough that they can maintain a pet, then by all means, they should have one, because the comfort and company of a pet is priceless, especially those who have exceptional health challenges that are often misunderstood by those who do not live with the illness or disease.