Despite everyone's intent at the beginning of the race to run straight through to the finish without sleeping, inevitably you probably will sleep at some point in the race. It's been done a couple times from start to finish without sleep but not often.
A couple hours of sleep is usually helpful to keep your head about you when packrafting Class III+ waves and figuring out how many miles you are off course. The dilemna comes with deciding when to sleep. Generally, you should be able to run and walk at least 16 hours the first day without stopping for more than a couple minutes. If you make it through the first night without sleeping, you can consider yourself pretty burly.
You'll gain time by not sleeping but you should also consider the extra effort involved for route-finding at night. It's not usually very efficient to travel when it's completely dark, even with a headlamp. Most racers stop moving when it gets too dark to travel. In a mid-summer race, this should be about 2am.
Most racers carry something extremely lightweight to sleep in. Some use a down coat or thick jacket that weighs less than two pounds. I've used a sleeping bag liner inside of a super light bivy sack for a sleeping system of less than one pound. Some people take a sleeping pad and nothing else.
Whatever you use to stay warm, keep your body off the ground as much as possible. Lay on your packraft, put your feet inside your backpack, put your shoes under your feet. If you brought a vest type life-jacket, put it on. If fact, put on all your clothes. Taking a dry pair of socks just for sleeping will usually keep you much warmer also. All these strategies will help keep your body heat from leeching away into the cold ground.
If you make it through the first night without sleeping, you might be able to catch a nap the next day when temperatures are warmer. Your sleep will be much more restful but you'll lose time by not moving. On some Classic routes, there are public use cabins to sleep in. The Solo Mountain cabin on the Nabesna to McCarthy route is one of these. It has a wood stove so you'll be warm and can dry out. The only danger here is the siren call of the bed and there's the danger of staying too long and losing significant time.
Waking up on the morning of the second day at 4am after two hours of sleep on the cold hard ground is difficult. You'll wonder why you started the race at all and you'll be ready to quit. Usually you'll wake up not because you really wanted to wake up and start moving again at 4am but because it's just too cold to sleep anymore. The only way to get warm is to start moving.
This is what a 4am wake-up looks like. Cold and miserable.