On GitHub you can use a git tag to publish a release announcement which will then appear on a release page (example) and release feed (example). If a developer has done this, you can subscribe to the feed to receive notification of releases rather than all commits.
Is it possible to do this on Bitbucket (hg and/or git)?
(There is an additional option to include binaries / tarballs in GitHub release announcements. I am not concerned with that feature or any others beyond a feed with announcement entries.)
Not currently (Q4 2014/Q1 2015).
Any feed issue is managed in "notifications".
The closest you have from feeds (for release or anyhting else) is:
Original answer, regarding the possibility to upload release files:
The BitBucket FAQ on "repository/file/upload size?" does mention:
Keep in mind Bitbucket is a code hosting service not a file sharing service. If a lot of your files are extremely large or if your files are binaries or executables, you should understand Git or Mercurial will not work well with them. You'll find that even locally your repository is barely usable. Moreover, Bitbucket can't display diffs on binaries.
For binary or executable storage, we recommend you look into file hosting services such as DropBox, rsync, rsnapshot, rdiff-backup, and so forth.
Still not sure what to do? Review this post on stackoverflow for more ideas.