Do they work together?
Fluff says that Alkahest Bombs do acid like damage...
Yes.
Sticky bomb refers to the Alchemist's bomb. A cryptbreaker is an archetype of the Alchemist class and the Alkahest bomb is a modification to the generic Alchemist bomb.
The Sticky Bomb works for any modified alchemist bombs. The splash damage continues to harm the target, doing the same damage type (fire or acid or cold, etc) as the original bomb did.