I've tried testing this, and interestingly it behaves differently for different status effects..

Acid works as you said. So does haste. With 40+ int Haste is 4 turns, except on characters with walk it off, it becomes 1 turn.

Peace of mind however is interesting. Normally its 3 turns. 40+ int it becomes 6 turns, but on a character with walk it off it will last for... 4 turns?! Would be interesting to see what causes this.

Edit did some more testing:
Fortify, magic shell, encourage, meld metal and soothing cold all seem to follow Peace of Mind's structure of 3 turns base, 6 turns with 40+ int and 4 turns with 40+ int on a character with walk it off.

Interestingly, skills that only affect yourself behave differently.
Flaming Tongues for instance is also 3 turns base, turned into 6 with 40+ int, but if your character has walk it off, it's only active for 2, which follows the base-1 turn formula of acid/haste/burning/wet/schocked/suffocating.

Also interestingly, the bleeding from Terrifying cruelty and sawtooth knife at 40 int also becomes 4 turns on a character with walk it off, seemingly behaving differently than other damaging status effects..

So the only exception to this, are skills that are 3 turns in base length, that also affect other people.