Lower than 0.7-0.6V voltage drop on sillicon diodes
Figure 1. Current versus voltage for various coloured LEDs with curve for nine series diodes shown in black.

The chart of Figure 1 is a little rough but it should get the idea across. With your 2.7k series resistor max current will be about 3 mA. We won't be able to see this on the graph so I'm going to discuss the case when the LED is lit with 20 mA.


At 20 mA we can see that a red LED will have a forward voltage drop of about 1.8 V. This means that the voltage at the top of the diode chain will drop to 1.8 V.
If we look at 1.8 V on the diode curve we can see that the current through the nine diodes is going to be very small. I had a look for low-current/voltage graphs for the 1N4001 diodes but none had graphs for less than 10 mA.




Figure 2. The 1N4148 small signal diode datasheet goes down to 0.1 mA.


Even the 1N4148 datasheet only goes down to 0.1 mA. If you extrapolate the graph you can see that for every 0.2 V or so the current will go down by a factor of 10. 



  So my question is, why does the power supply only "consider" the 1.6V drop across the LED and sends current accordingly, instead of "considering" the 6.3V-5.4V drop across diodes (which is what happens when you take the LED out of the circuit the circuit)?


It's not the power supply considering anything. The LED hogs the current and as can be seen from the graph will cause the voltage to drop to 1.8 V. That's all the nine diodes have to forward bias them and, as the 1N4148 chart shows, you won't get much current through them at that voltage.