Does registering in Editorial Manager® and indicating that I am available as a reviewer increase my chances of being invited to review manuscripts? Do editors check the database of registered users in Editorial Manager®, their keywords and ORCID records when selecting reviewers? I believe the majority of reviewers are assigned based on the references of the manuscript, the editor's personal preference and knowledge and the list of suggested reviewers. However, will merely registering in Editorial Manager® increase my chances of being invited? I am an early career researcher, with a few publications and some reviewer experience. The question refers specifically to journals that use Editorial Manager®, but it can be applied to other journal submission systems.
This depends on how the editor finds reviewers. Some (most?) editors select reviewers the way you described: from the references, the editor's personal contacts, etc. Others search the system. Editorial Manager allows the authors to select the subfield of their paper, which in turn can be matched to reviewers' interests. An editor who's searching the database for reviewers then can find you if you register.

One thing is certain: registering in Editorial Manager won't lower your chances of being invited (unless you have a track record of writing bad reviews, since your reviews will be tracked by the system).