Smoke detector position vs air register
You are correct to be concerned!
NFPA 72 (my cite is from the 2010 edition, but this rule hasn't changed in the last decade I reckon) 29.8.3.4 point 6 covers your situation:

(6) Smoke alarms and smoke detectors shall not be installed
within a 36 in. (910 mm) horizontal path from the supply registers of a forced air heating or cooling system and
shall be installed outside of the direct airflow from those
registers.

So, either the smoke detector or the air register has to move, lest airflow from the register create what you describe with a false-negative result due to smoke being blown away from the detector.