Not in the concentration typically used, which is about 1oz. per gallon or less.  There are 128 oz. per gallon, so the fuel stabilizer only makes up 1/128th of the fuel.  You could use two stroke oil in that concentration and it would be a 128:1 mix ratio, and also wouldn't affect anything.  I know guys who in fact use 2 stroke oil at 1 oz./gallon before winter storage because it coats and lines the fuel system creating a barrier that the ethanol and water can't get through.  The mix ratio is so low the car doesn't even smoke.  You'd never know it was in the fuel unless they told you.  BUT, if you do this you have to use conventional two stroke oil.  The synthetic and semi-synthetic stuff will fall out of suspension over time and you won't get the protection.  All I use for mix gas is synthetic now because it burns so much cleaner and keeps the engines cleaner internally, meaning less problems.  I just make sure to shake up the fuel ans before using them after they've been sitting. 

For fuel stabilizer, personally I like Startron (blue bottle sold at most shops that sell and service lawn equipment).  I add 1 oz. per gallon to all my mix gas for my weedwacker, chainsaw, etc whenever I mix up fuel (cheap insurance and I've yet to have a single issue with anything since I started doing this).  I put 1 oz./gallon in anything that takes straight gas when preparing for prolonged storage (tractor over the winter, generator, etc.).  I'd use it in my Mustang without hesitation, but its typically stored for a maximum of less than two months a year.  If its not snowing, and the roads aren't coated in salt I drive it pretty much year round as much as I'm able.  Cold isn't a factor for me; its got heat

Most small engines actually have fairly high compression.  Its how they are able to get a lot of HP (relatively) from such a small engine.  I always use 93 in all my mix gas.  My chainsaw has such high compression that it has a compression release to assist starting. 

As far as Sta-Bil the consensus around here is that it doesn't deal with the ethanol nearly as well as Startron.  Originally Sta-Bil was formulated to simply keep gas from going bad, long before we were all forced to run gasahol by the government.

That part of Canada that comes closest to Russia in the Arctic circle.