In my experience of importing some Japanese 100V 50Hz preheat fluorescent fixtures with HX autotransformer ballasts and series choke ballasts to try on standard North American 120V 60Hz domestic mains supplies, I have noticed that the ballasts were often running at around 15% above their rated line currents and I have experienced no ballast failures so far after I have been putting those fixtures into daily use for a few months.

Will a good quality inductive magnetic ballast with copper windings that runs at around 15% above its rated current have a high likelihood of failure if put into daily use over a short time period?

Generally what dictates the reliability is mainly the operating temperature, 2'nd significance is the dielectric strength if the design was "on the border" to start with (and that is also heavily accelerated by the temperature, by the way).

It will exhibit about 32% higher losses, so roughly 32% higher deltaT. So if the original ballast was designed to run at lets say 125degC with 25degC ambient, at a 15% higher current it become operating at about 157degC. That means 32deg higher temperature, so about 8x shorter lifetime if that was limited by the thermal degradation effects.
But if you compensate for the extra losses by better performing heat sinking so the temperature is not higher, there i would not expect any reliability degradation.

In my case, I have had my Japanese 100V 50Hz 32W preheat circline HX autotransformer fluorescent ballasts having a total power consumption of about 45W compared to the rated 40W power comsumption while I had a 100V 50Hz FL20S preheat fluorescent tube series choke ballast running at around 30W or so compared to the rated 25W power consumption. In those cases, the 32W ballast consumes about 12% more power than it should be and the 20W ballast consumes about 20% more power than it should be.