Yep. I only had one harness in the Miata, and at more than one track event I was forced to run without it until I was soloed.
Keep in mind also that harnesses are a wear item, and should techinically be replaced every 3 years for on-track use. They are stamped with a build date, and some track event organizers won't accept an out-of-date harness. Keeps this in mind when shopping, and make sure you get a harness with a recent build date, whether buying new or used.