Anything is possible (just not probable).
Yes, you could have some sort of a low resistance that MAY not trip the breaker and MAY heat up.
You could also get struck by lightning while being stung to death by bees and being hit by piece of space junk that fell off the Russian space station.
To confirm what was already stated: the specific NOS wire I use is MIL SPEC and has cloth covered rubber insulation.
This wire is SIGNIFICANTLY more abrasion and heat resistant than ANY "for domestic use" UL listed cord you could find.
It was ENGINEERED by Western Electric as POWER CORD for ULTIMATE durability and performance. It has been used in the most EXTREME of conditions, such as deserts, Arctic, and aerospace applications
I have some of this wire that's been in use for over 10 years and it shows NO SIGN of fatigue, cracking, or wear.
I have sold HUNDREDS of these cords and NOT ONE has failed in use to date.
They are HAND MADE in USA by either myself or one of my new employees. My employees are all students that are getting their degrees in electronics and I pay them $20/hour to start. No minimum wage slackers work for me (though I do live with 4 fairly lazy cats).
The cords go through SEVERAL inspections and tests along the way including a RESISTANCE TEST after they are assembled.
Personally, I would rather put my faith in a American with technical expertise that is earning a fair wage for their time than some uneducated 3rd world person that is cranking out UL listed products in some sweat shop for less than $10/day.
I would also be most fearful of ANY mass marketed "bargain priced" appliance that is UL listed. What that listing means is that is passed the MINIMUM requirements.
Most of what this UL listing stuff is about has more to do with product liability than with performance. If for some reason their is a product failure that leads to a law suit the company could state that they "did everything possible" and are therefore not negligent.
Let's settle this once and for all:
I challenge anyone to find some way to cause one of my power cords to burst into flame.
If anyone can find some way to make one of my power cords burst into flame while plugged into an outlet that is up to code with a proper circuit breaker I will give them $1,000.
Anybody up for the challenge?