The advice here is to start and go immediately. That's about how I've always done it. However, the idling engine is warming oil and coolant as well as all the metal, ever so slow though. Rationale is, the diesel fuel could be pushing you toward your destiny instead of being wasted.
If you have a hard-start (longer than normal cranking) on a typical morning now, not winter, well, the Injection Pump may be losing prime. Losing prime is more noticeable after the car sits overnight.
All GPs don't go out at the same time. If one or two GPs are out, the engine will idle pretty rough for a few seconds after you start it. If the GPs are all out, likely the Glow-plug Relay is the culprit. The GPs can be tested with an Ohm Meter without removing them. Off top my head, I don't recall the specs. Also, the GPs don't stay on very long after the engine fires-up ........ less than a minute. So, there shouldn't be any unburned diesel fuel coming out the exhaust pipe. Likely there is some condensate and soot accumulation. Lastly, the GP light is basically an indication that they've begun the cycle.
There are three Glow Plug/Heat Elements in the coolant flange on the end of the head..... only on the 5-speed. Those Heat Elements stay on until the coolant begins to warm-up..... likely controlled by the ECU based on data from the Temp Sensor.