yes...
Use just a ounce of 2 stroke oil, Marvel Mystery oil, even a 10W40 oil would work. All you are trying to do is to lubricate the top end of your motor by adding some oil to the fuel. asyour rings are trying to seat it is rubbing against the cylinder walls, if the piston gets hot the rings swell with the piston causing greater friction an dmore pressure...that is why when it cools down it starts easy again. adding some oil to the gas tank for the next month or so won't hurt anything...in fact when rings get worn out or your top end needs rebuilt you are usually smoking pretty bad because you are using hte oil for lubrication, it is passing past the rings and you are burning it off the walls of the cylinder. SO you can add oil for the rest of your motors life and never hurt it...really! The old timers use to use Marvel Mystery oil to the gas and to thier oil all the time to keep things lubricated...it doesn't hurt...I don't know how it would work if you had injectors...It may not work, but a shot of diesel fuel would...diesel is oil based as well...it smokes and it makes your bike run hotter, but it does lubricate and clean out a system...
If your gas cap comes off in your hand try another one to see...you might ask someone else on how to check one, but the answer is yes.., if htere is a vacuum being created it causes the same symptoms...it will also run lean an dquit...