Thanks for the replies, I was aware of the diode voltage drop, but didnt think of the potential drop from the arduino-pin itself...
The potential drop at the Arduino pin itself will be minimal. Any drop will be mostly due to the Base-Emitter Saturation Voltage of the transistor.
This is because the datasheet claims VOH to be 4.1V when the load on the pin is 20 mA. However, the transistor will be providing most of the current (its gain will be somewhere around 100). In this configuration, the output voltage on the Arduino pin should be somewhere around 4.4V.