No,the forward voltage drop is not constant for any PN junction .In silicon its typical 0.7 V at room temperature,the forward voltage drop of a PN junction depends on many factors,like type of semiconductor material used,voltage applied across the junction,temperature of the junction,current and their are many more.Forward voltage drop could be expressed by an equation known as diode equation or Shockley diode equation (search google for more info).
Long ago I used a transistor as a temperature sensor using its base and emmiter junction.Its junction voltage drop changes with temperature but the sensor was not so accurate because it was not linear.
It's like everyone saying that a diode has a 0.7V drop across it. When you look at a data sheet they list a higher voltage drop. It depends on the current going through it.
Assuming 0.7V (or 0.65V or whatever) across a forward biased silicon junction is just a rough approximation, or rule of thumb. It may be good enough for making rough estimates of circuit conditions, provided that you are dealing with fairly ordinary devices, carrying moderate currents at moderate temperatures.
More accurate prediction of junction voltages requires models based on the diode equation, with added representations of the less ideal behaviour of practical devices. This approach is used in circuit simulation programs like PSpice.