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Having the choke on adds more gas and sounds like one of your jets are plugged in the carb its making up for that. It shouldn't cause any damage unless its over fueling and can soak down your sparkplug and it wont run. But you should clean your carb as it will run better.

As long as the engine is not chugging out a lot of black smoke it likely won’t hurt anything. My guess is the float in the carberator is not set correctly so by having the choke on you get a rich enough mixture to produce power.

When your choke is on it restricts the incoming air entering the carburetor Venturi, effectively enrichening the air/fuel mixture. The choke should be turned off or opened as soon as a motor will run smoothly without it. If your motor needs the choke to stay running after warm up then you have a problem that needs fixed.  
Running with the choke on for long periods of time will cause excessive amounts of unburnt fuel in the combustion chamber which will blowby the piston rings and enter the engine oil causing contamination and eventually will be catastrophic to the motor.  
If the motor needs the choke on it needs the problem diagnosed and fixed, maybe you left the choke on by accident, in any case I would change the engine oil. If it’s badly contaminated and smells of gas you might have to do it again after running a while.  
As a side note unburnt fuel particles are highly pollutive to the environment so it is best to keep your motor properly maintained to avoid this.  
 
Edited by Farmergeorge, 2022-02-15 07:27:57

Kit from Amazon new carb,primer, spark plug,fuel line,fuel filter, for less than $40 tax incl. Put it on, primes it 4x to fill the bowl and started 1st pull! Was tired of messing with my old carb

If the noise you are hearing is the starter buzzing then it likely is not engaging. It likely has an ice build up and will not engage the fly wheel. A few minutes with a hair dryer on the starter will likely thaw it out. Otherwise try starting it with the pull cord.

Above post is likely correct, probably ice. Also check oil, if above maximum there may be gas in it. Also pull spark plug and check that combustion chamber is not full of gas, that would cause a hydraulic lock.