No, dermaplaning (using a blade to remove superficial skin cells and hair on the surface of the skin) will not cause increased hair growth. This procedure does not at all effect the hair cycle, which is regulated by cells deep within each hair follicle. Hair that has been exposed to "the elements" (ultraviolet rays from the sun), chemicals in our skincare products, etc. may seem thinner/less coarse that that comprising the "stubble" that you notice soon after shaving or dermaplaning. However, the individual hairs are still growing at the same rate and thickness as they would have before you shaved them since, again, you have not affected the cells deeper within the follicle that dictate the length of the hair cycle and the thickness of individual hairs.
So, you can rest assured that dermaplaning, as well as shaving at home, will not cause you to be more hairy in the long run.