Although it is very convincing (Cough cough) Charizard and Rhyhorn (Cough Cough), logic shows otherwise. Small cute Pokemon (Caterpie, jigglypuff) have higher, cuter cries, whilst big, fully evolved Pokemon (Charizard, Blastoise) have deep rumbling cries. Not a coincidence. If they were random, these cries would be all over the map in terms of sound. So no.
On a side note, there were only 37 different cries in r/b. Other cries were made by taking one of the base cries, and changing the pitch or otherwise.