Strictly speaking, no relevance.
However, in view of the fact that some posters had expressed agonized dismay, shock and horror
at the sole thought of such an initiative (establishing on localizer without being specifically cleared, when comms are too busy to query ATC and closely-spaced parallel approaches are in progress), I thought it might be of interest to point out that it's not an inconceivable course of action in some parts, and is indeed mandatory at some very busy international airports.
Having said that, and in answer to the OP, I wouldn't try this in KLAX (nor in any other port where such a procedure is not mandated, for that matter). You would be inviting disciplinary action
or at least a very severe talking-to
