So in reality, will I still get the base voltage equal to the voltage drop across the diodes if I put the positive Vcc at the top and ground at the bottom?.
In the case of the Current Source, as drawn, no.
It's a matter of what you use as a reference when making voltage measurements.
For instance, it is usual practice to connect one lead of the voltmeter to "earth/ground/0V/system common" or whatever it might be called on a particular diagram, for all voltage measurements, placing the other lead at whatever point you want to measure.
"Earth/ground/0V/system common" is the reference. It is the point to which all other voltage measurements relate, unless stated otherwise. e.g. Vbe is the voltage between base and emitter.
In all three circuits of your diagram, Vb, a base voltage, is measured between a base and earth. Ve, an emitter voltage is measured between an emitter and earth. Vcc is measured between the supply rail and earth.
You can use any point you wish as a reference, if you think it serves any useful purpose. In the Current Source circuit you can use Vcc as reference and measure everything with respect to it.
So, by putting one voltmeter lead on Vcc, the base voltage is equal to the voltage across the two 1N4454 diodes..
Measuring with respect to earth, the two voltages are not equal. But nothing has changed.
Using the same logic, In the Current sink circuit, using earth as the reference, the base voltage and the voltage across the two diodes are, obviously, equal.
However, using Vcc as a reference, the two voltages are not equal.
Sorry, my mistake. I meant the current flowing from emitter to base in the current source.
Yes, base bias current is from Vcc, emitter-base, R1, earth.
And there is the diode current from Vcc, the diodes, R1, earth.