The short answer is yes! Imagine how much more you can accomplish by removing the paperwork burden from your program. More time to think about the big picture and work with students. More accurate data because parents enter their sensitive data directly. More timely information for you because those data are immediately available.
Online registration means less, too — less errors, less time spent collecting and collating forms, less rejections due to conflicting requests.
Everyone is online now. Paper registration forms are a thing of the past. Adding online registration to your existing web site is simple and very cost-effective. People no longer accept the limitations of paper registration forms, having to take time during the day to stand in line, or even make phone calls. These people will gladly cover the extra cost of an online registration system for the convenience of browsing your schedules and locking in an interesting class at their convenience.
The long answer is "why not?", and only you can answer that.