@paulydoregon unless someone else can provide results and explanation, the answer is apparently no.
Regardless of being RS or E, from my tests, the same number gets generated.
It looks as tho the new number was generated either based on the old number or using the present 'real time clock', or some if/or option relating to both.
Note: These 3 sets of values are all different old saves, all from Sapphire.
My 0000 -> 9454 (four different sets of saves at different points in time all resulted in this)
My 92F8 -> 9454
My 9E97 -> D0C2
I did tests with Emerald as well, but it yielded a similar pattern of results.