peterb is absolutely right. I apply rooting hormone for two reasons:
1. to speed up root formation, which helps the plant to become established faster and in some cases is the only way to even grow a plant let's say from a cutting.
2. to protect the cut surface from possible invasion by pathogenic fungal organisms, e.g. Rhizoctonia spp. et al.
Rooting hormones come in various strengths. Those that can be used for harder-to-root cuttings having the highest amount of active ingredient. There are some hardwoods that are almost impossible to place in the soil to form roots even with the high-dosage rooting hormone applied. For most cases you will be fine using the general strength version. I do not believe that the compound will in any way hurt a plant if applied to it. The longer a cactus sits in the ground, however, without being able to form roots the more likely it would be - in my opinion - to not survive. Transplanting is already a shock to plants and when you transplant something that has no roots to pick up nutrients and water you have even a higher chance than normal of losing your specimen.
Be aware, however, that there are differences, even among cacti, when it comes to rooting. As Kansas Opuntia Bill can tell you, a good number of prickly pear cacti will easily root. If a pad falls off and stays in contact with the soil it will oftentimes form roots. No rooting hormone is needed in that case. As someone on the forum also pointed out on another post, a cactus left sitting in the open outside a pot will often start to form roots, as if to "look" (search)for growing medium. But you have to take my advice "with a grain of salt". Although I do have a Master's degree in horticulture, I do not have the greenest of thumbs. Maybe that is, because I do grow all my plants outdoors and thus have less control over them. I just pulled a good-sized Echinocactus horizonthalonius plant out of the ground that had succumbed to a rot. I have heard, that that kind of plant is rot prone, although it looks tough on the outside. Probably the location I had it growing was not ideal. On the other hand, it was also a rescued cactus that I transplanted last spring. Maybe its root system had not calloused (healed) well enough before I placed it in the ground. Coming back to the rooting hormone question: I am a proponent and have had good luck with it in the past.