Working in the part of the TMA where this happens, I would say that although you are cleared eventually to 6,000ft you have to make mandatory level offs at specific altitudes.
If you call me and say that you are climbing to 6,000ft i and almost every person that I work with will assume that you have missed the stop off (and that you are using Jeppeson plates
). I would then tell you to stop climb at the initial altitude and if you were very close to another aircraft, I would probably write a safety observation about it!
The number of level busts in the LTMA caused by this very type of SID and the fact that pilots miss the initial cleared are too numerous to mention.