Your phone will still work, but you did shorten your battery life by about 10%. Although some chips might have melted a bit, they will continue to work. Also, instead of getting, say, 6-8 hours out of the battery, you will be getting about 5-6.
Other than that, your phone is undamaged.
If that was the case the warning message would pop up sooner. No point in having something to prevent damage pop up after the damage is already done.