Mendeley has two types of groups- Public and Private According to their website
Create and join Public Groups to share knowledge and discuss new
research with others with similar interests. You can also create
Private Groups that are only visible to invited members, letting you
share information securely.
When discussing setting up a profile it promotes the idea of you been able to publize your publications through mendeley.
Publications - Adding your publications to your profile allows you to
publicize your work to a global audience. You can add your
publications to the My Publications folder in Mendeley Desktop or Web
Library, or upload them directly via your profile. You can also add
the entire contents of your Scopus Author Profile in one batch
On another page it states that you can promote your work publicly
By connecting your Mendeley profile to your Scopus Author Profile, you
are able to claim your work as identified by Scopus. This allows you
to publicly promote your authored work, and access a wealth of data
provided by Scopus - as well as several other Elsevier services - in
the form of Stats.
For your publications to be seen publicly you probably would have to edit your privacy settings and select for you publications to be seen by everyone. Picture source