Technically, yes. Booklets can be sent via direct mail - though most forms of it would require an envelope or sealing tabs to help keep it together. Some types of mail do not. It's uncommon, but very cost effective to use saddle-stitch booklets as EDDM mailers.
Should you decide to send magazines to specific addresses without envelopes, you'll need to use sealing wafers and address labels to get it through the mail.
If you're interested in how to accomplished your mailing with your printed booklet or catalog, then fill out the contact form at the bottom of this email.