The carb cleaner can further dilute the gas-oil mixture, making it sort of light on oil. If the squirts are kept short and the saw isn't working hard or screaming at wide-open throttle, you probably won't do any harm. Remember the gas-oil mix has enough oil to lube the engine at full throttle under load, and most any other time is too rich on oil.

Spraying carb cleaner in a chain saw won't do much.  The carbs don't have exposed jets and there is no float bowl....they are diaphragm carbs.  Anything you spray in the carb throat is most likely just going to go straight through the carb without touching or cleaning much.

I have cleaned a lot of chainsaw and weedwacker carbs in my day.....I worked at a dealer in the 70's and I have continued to work on the local neighbors and friends saws since then.  Most of the work was a result of the saws sitting dormant with fuel in them....and they sat too long and the fuel congealed or the diaphragms have become stiff over the years.

Seafoam might work....but there is  danger in running a 2 stroke engine with a fussy carb.  If the engine is not getting enough fuel it is also not getting enough oil.  It is common for 2 stroke chainsaw engines to score the piston and cylinder if you continue to run it without the proper fuel/air ratio.  Trying to force a poor running chainsaw into healing itself is never a good thing.

I heat with firewood and own 3 saws with bars ranging from 12" to 32".  If I am not planning on cutting the saws get the fuel dumped out, then the saw is started and allowed to idle until the engine stalls to run the fuel out of the fuel lines and carb.....Stihl recommends in their owners manual that you do this for storage.  My saws always run just fine the next time I put fuel mix in them.