Absolutely not, engine needs to breathe. First check oil level on dipstick if it's overfull & smells like gas you have a carburetor problem. If oil level is ok check spark plug by removing & inspecting visually. Check fuel cap vent for being open & free of dirt. If your mower is over a year old you need to adjust valves with engine cold. Post engine manufacturer as well as all numbers from engine data plate.
No I did not miss your point, air filter should be replaced yearly unless you have dusty conditions then more often. Have you cleaned underside of deck & removed & inspected blade for cleaning, dressing up with a file & balancing blade. If your blade is buggered up & distorted it needs to be replaced. Model number is missing a number if B&S engine, six characters, model xxxxxx, type xxxx, trim xx & code number.