Can ATC Instruct, "Cross IAF, AOB on ILS" ?

[tomgoodman]

Close, but not reliable

That used to be the case with some of the R25L/R arrivals at LAX. If you crossed CIVET on the glide slope and followed the GS all the way down, you would put yourself a few hundred feet below the minimum altitude for one or two of the many fixes on the way down.

Yes, that was a well-known "gotcha" approach, because sometimes it looked like the GS was going to comply with a stepdown restriction --- and at the last minute you saw that it was going to be too low. We were told that while the localizer was indeed certified for guidance a long way out, the glide slope was not.