The answer depends on whether you're talking about a snapshot or a release build.
Release builds have a version that doesn't end with "-SNAPSHOT", and they're final and immutable. Once installed to any repository, Maven will never update them. To your question, that means that if a dev installs a release build locally, it will never be updated from any remote repository.
Snapshot builds are always eligible to be updated from any repository. By default, Maven checks once per day for new snapshot versions, so if someone installs a snapshot locally, that snapshot will exist until Maven does its next check for snapshot updates. Then, if a newer version is in any remote repository it checks, the local one will be overwritten. You can force maven to update snapshot artifacts with the -U
command line option.