People write their addresses on a paper form to sign up for my list. Is that verification?
Unfortunately, paper forms do not count as address verification. You may not send to addresses from paper forms unless you also separately verify the address.
The main reason is that you have no way of knowing whether the addresses contain "typos": a surprising number of people write down their email address incorrectly or illegibly. Also, people sometimes write down the addresses of friends who they think might be interested in a list — but if the friend has never heard of you, that will lead to spam complaints.
In fact, addresses written down on paper lead to far more complaints than other kinds of addresses. List owners are often surprised at how many complaints these lists generate, even when they seem "squeaky clean" because every address was supposed to be the address of someone who paid money to join an organization.
So if you have addresses written on paper, use Mailman's invitation feature (or verify the addresses another way if you don't use Mailman). This makes sure that the person at that address really wants to be on your list, and guarantees that you don't inadvertently send spam to strangers just because someone wrote down an address that wasn't their own.
This system also benefits you in another way. You'll be able to see how many people verify their address and complete the signup process, so you'll know which addresses are correct and which ones have a problem.
This lets you contact the people who don't complete the verification process to get the correct address or see if there is another problem preventing them from receiving email messages from your list. If you subscribed people without verification, you would never know if some of the intended recipients aren't getting the list messages.