This is the sort of thing I had in mind when I suggested a kludge. The deficiencies that you described suggest that a kludge would have rudimentary capabilities compared to a more sophisticated machine.It is possible to build a general purpose computing machine out of thermionic tubes and ferrite core memory so an emulation of modern mobile phone circuitry would also be possible. However, it would likely be enormous and use a lot of power if the smallest available tubes were those of the sort from before the transistor age. The main problem would be that its switching speed would be far too slow to do the necessary modulation, demodulation, error correction, encryption, and decryption in real time.
This suggests the limitations of trying to imitate something from a higher technological tier.