To ease your mind about this, it would be a very good idea to call the place where you will be having this done, and talk to them about your concern. I am confident that there are many who, even if they don't have trouble falling asleep on a daily basis, will be afraid they won't be able to fall asleep in this situation.

I had a sleep study done about 15 years ago. At the time, I was taking a med to help me sleep and they told me I could take it that night, but I didn't because I didn't always need it and I didn't want it to be a factor in the study results.

One thing that helped is that while it is anxiety-provoking beforehand, once there and talking to and being cared for by the technician, seeing more of what to expect, getting the elctrode connections stuck on (usually some humor there because it feels humorous!), and then getting squared away in bed with your book or TV or iPod, you feel relieved to have made it through the uncertainty and you really feel ready to climb into the bed with the fresh, clean, cool sheets and rest....