IT would not hurt but it may not necessarily make any difference.
I have seen a lot worse than yours where fuses have not blown
The coils & wires are not designed to run at full output for hours on end .
So if it is running at the full 5 or 9 amps all the time the engine is running the wires will overheat .
Several things cause stator melt downs the most common are below .
1) debris build up under the flywheel causing physical contact between the flywheel & laminations
2) running the mower with too much electrical load such as a short or flat battery
3) wiring fault &/or including bad diodes, failed rectifiers & bad rectifier grounds
4) motor overheating
Of the ones I have replaces , a faulty or flat battery has been the primary cause for the majority of melt downs
And I have seen a lot worse than yours
And FWIW I have has more than one customer refuse to replace a bad battery then expect me to replace the burned out stator as a warranty item.
One even make a claim with the consumer affairs department , it was naturally declined as I always not problems not fixed on my invoices
Their claim was based on "Face book experts" who claimed you did not need a battery to run a ride on mower engine
Thank you,bertsmobile1. Since the stator isn't totally fried, as in a dead short circuit, I believe you may be correct in that it's running at near maximum output at or near 100% of the time. The battery a couple of years old and may be due for replacement. It's been my experience that mower batteries are a short-lived item, unlike auto batteries and difficult to load-test. Also, I shy away from "experts" on facebook. I'll watch a video to see how something comes apart, but most 'advice' is suspect , to say the least and sometimes downright dangerous!
Addendum:
I'm going to replace the existing old battery before Thursday's mow, to be on the safe side, what with the replaced stator and regulator. No point taking the chance of smoking the replacements!