Unfortunately, you can't get stats on the number of views on documents unless were able to embed the tracking code. To get the tracking code, log into OLSB. Go to Reports > Administration > Get Code. Keep in mind the tracking code will only work on web documents such as html, htm, aspx so if you're using a .doc file this will not work.
As an alternative to a document serving as a registration form, I suggest creating a web form in Office Live. This way users can fill out the information online. The registration will be inserted into a Office Live Business Application and if you like a workflow can be setup that will email the registrants their information in which they can print or save if they like. Also, because the registration form will be on a web page web stats will be available to let you know how many views you have.
For more information on how to create a form in Office Live, visit my blog post on the topic - http://tutorialslive.spaces.live.com/blog/cns!1DB0472F087736FB!151.entry
I hope this helps!
Norris