Yes, driving with the handbrake on will cause brake overheating and a burning smell. If done for a long enough period of time it can cause damage to the seals in the caliper, which may require a caliper overhaul or replacement. In most cases though, simply letting it cool off will restore it to normal operation. You'll want to check it for over heating on your next trips in case it's been damaged and starts sticking on its own. You'll also want to keep a close eye for any brake fluid leaks from the overheated area. Also, note that if the brake pedal feels soft or spongy that you at a minimum need to bleed the brakes and may also be a symptom of a leak that needs to be repaired.