Yes! Online hatcheries have streamlined the shipping process so that most chicks survive. They often include an extra or two to offset losses, but most or all of your baby chicks will survive through the shipping process.
One reason chicks can survive being shipped in the mail is that they have all the food and water they require for the first 72 hours from the nourishment of the egg itself.
Also, most online hatcheries will only ship orders of 25 or more chicks because they keep each other warm during shipping. A few online hatcheries will ship smaller orders of baby chicks. They use heat packs to keep them warm through the shipping process.
When your chicks arrive, the hatchery will include instructions. Generally, you'll dip their beaks in the waterer gently so they know where the water is, and you might feed them a special "gel" or enrich the water with electrolyte and/or vitamin powder to minimize the stress of shipping.