I'm afraid no.
As you mentioned the openstacklib::db::mysql defined type includes the mysql::server,
which triggers installation and configuration of mysql.
This is basically because the implementation uses some resources like mysql_user
imported from puppetlabs-mysql and these resources are designed to work in the node
where mysql is deployed by mysql::server. (Especially the ~/.my.cnf file created).
Technically speaking you can remove that include as long as you can prepare all of
the required resources with these resources but that'd be quite tricky.