It takes quite a while for the gasoline to "varnish". The fuel might go bad in a few weeks (not varnish), but the motorcycle should still start & run if it isn't too old. Before trying to start, be sure to prime the carburetors beforehand using the petcock selector, in case the fuel level in the carb bowls is low for whatever reason, such as evaporation. The engine may be a little hard starting but it should start; it may run poorly at first but should improve as the fuel from the tank refills the carb bowls. All of this has been my experience, but my motorcycle is in a good state of tune & normally starts the second I touch the starter button. so old fuel doesn't cause a problem. If your motorcycle is already hard starting, then dank fuel could be troublesome.
For storage I would drain all of the old fuel from the carburetors & fuel tank, then refill with fresh fuel. I would to prime the carburetors to fill them with fuel. You could also add a fuel stabilizer, but I don't use that stuff as we can have good riding weather year round.
Fuel freshness is dependent upon time, temperature & quantity. Fresh fuel burns better than older fuel.
Higher temps cause fuel to go bad sooner than cooler temps. in summer you have to be aware of that. Winter time isn't as big of a problem.
Large quantities of fuel last longer than smaller amounts. so the gasoline in the carburetors can go bad before the fuel in the tank. Sometimes I'll drain the carbs, then prime to refill. then burn the old carb fuel in the lawnmower.