Of course it is. The fact that the nails are naturally very short, or bitten nails are involved, are no obstacles to have an artificial nail on them. If someone has short nails, the template used for artificial nail construction can be applied the same way, or even tipped technics can be applied, which results the construction of same nice and aestethic nails.
For bitten and here-there damaged nails, there are gels exists, which are skin friendly and developed for exactly such cases. All of them sticks very well and equally durable like an artificial nail constructed on a healthy, intact nail.