Go for it..will only help it if anything..even if it had a catalitic converter,a 1/2 gallon is nothing ..it'll lube the top end and rings..a pint of marvel mystery oil dont hurt anything,and theres a lot less oil than that in that amount of 2 stroke mix..
I accidentally put a 1/2 tank of diesel in both my 72 K5 and my 69 GTO many years ago,at the same gas station,that had poorly marked pumps and the diesel one right next to the gas pumps rather than on its own little island like the others...

..didn't make the 60 mile commute to work those 2 mornings,I got maybe 5 miles up the interstate and they started pinging at first,them slowing down,white dense smoke billowing out behind me..barely made it back home!..spent the rest of the morning draining the tanks out into a plastic wastebasket,the only container available that would hold that much fuel!..
It took a few tanks of fresh gas and a new filter before they ran good again,once they cleared out though,they never ran better!...
Ive experimented with my one cylinder air cooled engines and found that my old Briggs & Stratton on a tractor I have will run on just about anything flammable...
I've run it on mineral spirits,laquer thinner,enamel reducer,diesel fuel with a bit of gas added, and charcoal lighter fluid...one day I ran it ran dry way out in the woods,all I could find anything like gas was tikki torch fuel..it didn't run great on it,and started hard,but it was better than pushing that 700 lb beast out of the woods 800 feet back to the garage!..
One day at a small engine show not long after I did that,I saw an old Briggs that had a dual gas tank,with two gas caps!..--one side you filled with gas,the other side,kerosene--you started it up on gasoline and once it warmed up good,you shut the gas off and opened the kerosene valve and it ran on kerosene..guess farmers liked using that because it used to be cheaper than gas..
Back in my youth when I had a go-kart,we used to put that cox airplane fuel with nitromethane in the gas tank..it was like nitrous ,the muffler glowed red and shot blue flames out 3 feet long!..

..those were the days..