The answer is ...
The question is "Is it acceptable under ICAO 4444 to use rates of climb/descent for separation in a non radar environment?" The answer is a qualified yes. It all depends on the air traffic environment (e.g. route structure etc) and the circumstances (e.g. aircraft types involved; weather etc). The most common use is to specify rates of climb so that vertical sep. is maintained between two aircraft and this is normally done between two successive departures.
Procedural approach control was quite common in the UK back in the 1960s and I was fortunate to do my training at Edinburgh (1964-65) when there was no alternative! It really made you learn the basics of being a controller!