Does asthma ever have a negative effect on a person's sense of smell?

No: Asthma is a disease of the small airways of the lungs, smell occurs at the level of nerve endings in the nose. Having said that, allergies which can affect your sense of smell can set off asthma attacks.

Sometimes: Samter's triad is a complex of moderate-severe asthma, nasal polyps & allergy to Aspirin & other nonsteroidal anti-inflammatory drugs. Polyps are benign growths in the nose that obstruct the openings to the sinuses leading to recurrent sinus infections and prevent air from reaching the sense organ for smell located in the roof of the nose. So patients with samter's have asthma & can't smell.

Possibly: It is not unusual for asthma symptoms to accompany seasonal allergic rhinitis, or seasonal allergies. The congestion associated with allergies can lead to decreased sense of smell.