Yes, if users want to receive an email for every post that’s created on the site, including their own posts, they can enable mailing list mode. This is done from the Emails section of their preferences page. For users to receive emails for their own posts, they need to be sure that the “Send me an email for every new post” option is enabled. The other option is to receive an email for every new post except the user’s own posts:
Note that before users can enable mailing list mode, you need to be sure that the “disable mailing list mode” site setting is not enabled on your site. I believe that setting is checked by default:
Also note that you can enable mailing list mode by default for all the site’s users from that setting’s page. Users can still disable mailing list mode from their preference page if they wish.
I guess it’s also worth noting that mailing list mode can generate a lot of emails. If your Discourse site is hosted, it’s possible the hosting provider either prevents it from being enabled, or that you will run into issues with hitting the limit of the number of emails the hosting provider allows to be sent from the site on a monthly basis.
If mailing list mode is not enabled, I don’t think there’s a way to receive emails for your own posts just by watching a category. When watching a category you’ll receive emails for replies to topics you create, but won’t receive an email for your original post in the topic.