The ability is this:
Assuming that close means 60-80%, yes we could "regenerate" the nutrients fast enough.
Limbs within Minutes. Assuming ten minutes for the Elk and, let's say 20-30 for us, and assuming that not using oxygen requires 10X nutrients because it's anaerobic cellular respiration, then we'd need to create enough nutrients for ten meals for every meal that the oxygen would be unlocking. So, if a whole chicken could take us an entire twelve hours, and a limb takes us half an hour at the most to regrow (Going off of worst case estimates here), and, because we're presumably a thin little girl, it takes two limbs to equal a chicken, that means that one limb could provide us the nutrients for 36 minutes. (6 X 60 = 360. 360/10 = 36)
It takes us 20-30ish minutes to regen a limb, and 36 to require the same amount of nutrients for feeding our cells, so unless the ability's utility was misrepresented, We don't technically need to breathe, although it will drastically slow our regeneration. Of course, we don't know this, but it's a nice ability.