no... never put injector cleaner with your 2 stroke mix. Im no chemist but I dont think detergents and lubricants should be mixed togather.
For the record... unless you ride very frequently, its easier to mix a small amount of fuel at time instead of a whole gallon or 5 gallon jug. I use a syrenge and a measured funnel with a valve I bought at autozone and pour it right in the tank. You can find very precise ratio calculators online that will tell you exactly how many ml of oil to gas.
I got tired of old stale gas sitting in my garage... its better for your bike too. You shouldnt let mixed gas sit for long periods of time.