When the randomTickSpeed is increased by a lot it seems the acculumation of snow in cauldrons is not affected at all.

How to reproduce

1. Create a new world with single snowy biome, e.g. snowy mountains.
2. Place cauldrons. (Possibly also place bamboo for comparison.)
3. Run:

   /weather rain
   /gamerule randomTickSpeed 3000 
   

   →  The cauldrons do not seem to fill at a faster rate. (Hard to test exactly, due to high intervals!)