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 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 may have to manually adjust symlinks in your custom dir. Symlinks (on Unix) in the binary directories point to scripts that can run on any platform. When and if the target of a symlink changes location for whatever reason, you would need to update the symlink in your own directory.
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: