BM - I guess your question is really about 'safety' and not the ATC side of things?
Most airline SOPs preclude descent on the GP before you are 'established', some allow descent when within 5 deg of the localiser. As long as there are no ATC considerations, and as long as you are quite CERTAIN you have no terrain or airprox problems, there is nothing safety-wise stopping you. It does happen that for various reasons LOC is not 'captured' before GP intercept and provided all the above are OK, it is OK, but, no, it is not 'NORMAL'.
I'm not sure whether 'opnot' answered in 'ATC' one of your other threads (Tech Log) about ILS capture to your satisfaction, but in relation to the a/c you saw 'fly through' the localiser- as he said - if the arrival is from the south and for R06, the FULL MIRSI arrival goes through the c/l before the approach is commenced (MIRSI being north of the c/l) but ATC often 'short-circuit' the procedure to vector from the south, or occasionally having just passed through the c/l but not got to MIRSI. Maybe this will explain your query in Tech Log?