I am not in any way giving legal advice, just my opinion...
There are certain "norms" in our industry--when someone enters their email address to get something free for example, they already know and expect they will be emailed repeatedly by the list owner. So a little explanation such as "we don'r spam", etc is enough.
For what you're trying to do, because it's outside of those norms, requires more explanation. Even if it's legal, you will have a lot of people very mad at you because I can promise you they won't read your terms. Some people get mad from 1 single email after they've signed up, taken the free gift, and agreed to e emailed--those types will blast you with awful comments and mail.
In this case I think it's better to get lower response and make sure people are clear. Just my 2 cents.