It is possible to install and use TeX Live with binaries that are not part of the original distribution. The most common case for this is when you are on a platform which the original TL distribution does not support.
Nelson Beebe has built an extensive collection of binaries. They are available by http(s), ftp, and rsync. The parent README there gives details.
Robert Alessi provides binaries and support scripts for a native TL installation on OpenBSD.
Given a set of binaries, here are the steps to use it:
Regarding subsequent TL package updates from the net: ensure that you have wget, xz, and xzdec available in your PATH; otherwise, TL will have no way to download or decompress packages.
Also, there will be no updates to the platform-specific packages in TL, since the custom platform doesn't exist in the canonical TL repository. Therefore, you will have to manually adjust symlinks in your custom dir if you want them to stay updated.
For example, if a new package is released with a new script that is added as a symlink to TL's own bin/ directories, you will have to add the symlink yourself to your custom bin directory. Likewise for deletions and changes.
Robert Alessi's OpenBSD support provides command for updating script symlinks (tlobsd mksymlinks).
If you want to install a second set of custom binaries (from, say, /tmp/barbin), you first have to manually rename the first set, like this: