Obviously, but the etec does "fog" itself with injection oil. It is a build in feature of the etec motor.
In regards to premixing for storage, I don't know if it would help, but it surely wont hurt anything. I would premix, and run the sled to get it running the pre-mix through it and additionally coating the bottom half of the motor. Then kill the motor with fogging oil.
As usual, everyone has their own storage practices and procedures. Fogging, frequent start ups, pre-mix, sta-bil, sea foam, etc etc etc. It does not really matter what your plan of attack is. The main point is to make sure all internal parts stay coated in oil during the off season, and this can be accomplished in many, many ways.
I usually end up with my sleds in enough pieces over the summer, that I will ocassionally spray extra fogging oil, or dump some two stroke on to the rods, and crank bearings through the reed cavity.