It is both yes, and no. CAN-SPAM do only apply to electronic mail messages, usually shorten down to email. However...

In late March, a federal court in California held that Facebook postings fit within the definition of "commercial electronic mail message" under the Controlling the Assault of Non-Solicited Pornography and Marketing Act ("CAN-SPAM Act;" 15 U.S.C. § 7701, et seq.). Facebook, Inc. v. MAXBOUNTY, Inc., Case No. CV-10-4712-JF (N.D. Cal. March 28, 2011).

There is also two other court cases: MySpace v. The Globe.com and MySpace v. Wallace.

In the later, the court concluded that "[t]o interpret the Act in the limited manner as advocated by [d]efendant would conflict with the express language of the Act and would undercut the purpose for which it was passed." Id. This Court agrees that the Act should be interpreted expansively and in accordance with its broad legislative purpose.

The court defined "electronic mail address" as meaning nothing more specific than "a destination . . . to which an electronic mail message can be sent, and the references to local part and domain part and all other descriptors set off in the statute by commas represent only one possible way in which a destination can be expressed.

Basically, in order to follow the spirit of the law the definition of "email" expanded, with traditional email like user@example.invalid being just one example of many forms of "email".