I just tested and you do need it to be out to "consume" the 10-30 sec cooldown. The duration won't run if it's vaporized.
That being said, if the Homu doesn't auto follow you (and probably die along the way), the VIT buff can be useful since it'll just keep applying it. Just a situational thing really. Not really groundbreaking or anything I'd say but is nice if you want "perfect".
I think the only Homu you can actually use to tank FOR you is Eira, where you Overboost to get really high flee on the Eira. Homus don't get flee penalty so with this they will be able to dodge mobs of monsters and even MVPs sometimes.