For the record, the "package tree" your refer to are typically called repositories (repos). If it is from Launchpad, it is called a PPA.
If you install an older version of a package manually (download a .deb file and install it with
sudo dpkg -i), then the high-level package managers (
aptitude, Synaptic, the system update manager, etc.) will prompt you to update to the latest version of the package.
If you install a newer version of a package not in the repos, nothing (else) will happen. Since the version installed is higher than the highest version in any repo, the high-level package managers will consider it "up-to-date". When a version higher than the one you installed becomes available, the package managers will prompt you to update to the latest version. Note that if the version in the repos gets a security update and the version number is still less than the version you have installed, you will not be notified of it in any way, since your version is higher than the existing version.
If you install a package not in the repos at all, then there won't be much of an impact, except that you can manage it from a package manager. (In this case, "manage it" would mean that you can remove/purge it, since that the only action available for such packages.)