Certainly, provided you have an alternate e-mail address that is not free. Aside from ISP e-mails, school, personal domain (webmaster@ or admin@), occasionally work, and other paid e-mail addresses are also accepted. If you lack all of these, perhaps you have a family member or friend whose e-mail address you can borrow? You only need it to initially retrieve your password, and after that you can set a free "preferred" e-mail to use.
Actually I know of a few ISPs who offer 'budget' subscriptions where you just get the connection, no email/webspace etc. And a few years ago I used a connection that we got for free from my dad's job that didn't come with an email address.