My goal is take the outcome class probability predictions from another model (or wherever, really), and use them as an offset in h2o.gbm with distribution = "multinomial".
I noticed in the nnet package, the multinom() function allows for an offset with as many columns as there are outcome classes (K). Does something like this exist for h2o GBM's?
No, offsets for multinomial GBM is currently not supported, mostly because of the API implications (offset_column would change semantics everywhere in the code), but it wouldn't be hard to implement otherwise.
The only option right now is to use the offset columns as additional predictors.