What will happen if for a BJT transistor it's Emitter terminal is treated as collector and collector as Emitter in a common Emitter amplifier circuit?
It will work but will have a lower \$\beta\$ (beta)
The BJT is formed by two p-n junction (either
Wiki about BJT: look especially the section
Another note: classical BJTs are created stacking the three regions in a linear way (see picture in the left), but modern bipolars, realized in surface (MOS) technology, will have also a different shape for collector and emitter (in the right):
In the left a traditional BJT, in the right a BJT in MOS technology (also called Bi-CMOS when both transistors are used in the same die)
So the behavior will be even more affected.
What clabacchio missed in his answer is that the inverse mode of the BJTs can be useful in some schematics.
In this mode BJTs have very low saturation voltage. Several mV is a common value.
This behavior has been used in the past for building analog switches, charge pumps and similar, where the saturation voltage determines the accuracy of the device.
Now MOSFETS are used in such applications.
If someone wants to make experiments, note that not every BJT can work in inverse mode. Try different types, measuring h21e.
But if the model is suitable, h21e can be greater than 5..10, which is pretty good value. To put the BJT in saturation, Ic/Ib should be 2..3;