It depends.

Authors that are registered users:
If an author of the paper is

• a registered user,
• known to be the author (see Claiming Authorship), and
• has not turned off email communications,

then yes, we will contact them.

Non-user Authors:
To avoid spamming anyone, until an email address is claimed by a user, we will only ever contact that email address at most once. E.g. if a user posts a question about a paper that includes an unknown email in it, we will email that author to let them know. We keep a list of all emails that we've contacted and will not contact them again for any reason unless the email is claimed by a user.