Kudos for supporting TOTP (what Google Authenticator uses), I hope other services follow their lead.

Previous discussion here: https://news.ycombinator.com/item?id=4436253

Reluctant to enable until I know how it will affect my desktop. Will I now get a prompt every time I restart?

No, you'll only get prompted on desktop/mobile the first time you link your account. If you already have a linked desktop or mobile app, it will continue to work without a prompt.

You can also see all of your currently linked devices here: https://www.dropbox.com/account/security

Dual authentication only occurs when you would normally be asked for a password, so assuming you have already linked your computer, you won't need to authenticate again.