Will you get more spam from being subscribed to the Arlington List? The short answer: probably not.
The longer answer: If you never post a message to the list, there is no way for anyone, whether a member of the list or not, to obtain your e-mail address, so there is no risk of getting spam as a result of your list membership. If you post a message to the list, it is possible, though very unlikely, that another member of the list will use your e-mail address to send you spam, or will forward your message to someone else who use your e-mail address to send you spam. The list archives are kept private, in part, to keep automated robots from harvesting the archives for email addresses to spam.
Note: If you join the cast of characters, a public web page, you expose your e-mail address to the public, and your e-mail address may be obtained for the purpose of sending you spam. Email addresses are obfuscated on this page, which reduces the chance of them being used for spam, but it's still possible. See also Cast of Characters